jet comonad

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## Idea

In a context $\mathbf{H}$ of [[differential cohesion]] with $\Im$ the [[infinitesimal shape modality]], then for any object $X\in \mathbf{H}$ the [[base change]] [[comonad]]

$$
  Jet_X \coloneqq i^\ast i_\ast
$$

for base change along the $X$-component of the [[unit of a monad|unit]] of $\Im$

$$
  \mathbf{H}_{/X}
  \stackrel{\overset{i^\ast}{\longleftarrow}}{\underset{i_\ast}{\longrightarrow}}
  \mathbf{H}_{/\Im(X)}
  \,,
$$

may be interpreted as sending any [[bundle]] over $X$ to its [[jet bundle]].

{#Kock10Remark731} This characterization via base change is more or less implicit in ([Kock 10, remark 7.3.1](#Kock10)) (to translate from the pull-push $(p_2)_\ast p_1^\ast $ shown there, as in ([Deligne 70](#Deligne70)) use that in a [[topos]] the [[epimorphism]] $X \to \Im X$ is [[effective epimorphism|effective]] and then use the [[Beck-Chevalley condition]] to get the push-pull shown above.)

$$
  \left\{
  \array{
    T^\infty X
    &\stackrel{p_1}{\longrightarrow}&
    X
    \\
    \downarrow^{\mathrlap{p_2}} &(pb)& \downarrow^{\mathrlap{i_X}}
    \\
    X &\stackrel{i_X}{\longrightarrow}& \Im X
  }
  \right\}
  \;\;
  \Rightarrow
  \;\;
  ((p_2)_\ast (p_1)^\ast \simeq (i_X)^\ast (i_X)_\ast)
  \,.
$$

$T^\infty X$ is the [[infinitesimal disk bundle]].

## Properties

The [[Eilenberg-Moore category]] of [[coalgebras]] over the jet comonad has the interpretation of the category of [[partial differential equations]] with [[variables]]  in $X$. The [[co-Kleisli category]] of the jet comonad has the interpretation as being the category of bundles over $X$ with [[differential operators]] between them as morphisms ([Marvan 86](#Marvan86), [Marvan 89](#Marvan89)).

## Related concepts

* [[topos of coalgebras over a comonad]]

* in [[Borger's absolute geometry]] a similar base change as above is interpreted as the [[arithmetic jet space]] construction.

## References
 {#References}

In the context of [[differential geometry]] the comonad structure on the jet bundle construction, as well as the interpretation of its EM-category as that of partial differential equations, is due to

* {#Marvan86} [[Michal Marvan]], _A note on the category of partial differential equations_, in _Differential geometry and its applications_, Proceedings of the Conference August 24-30, 1986, Brno ([[MarvanJetComonadPDE.pdf:file]])

> (Proposition 1.4 in [Marvan 86](#Marvan86) needs an extra "weakened transversality" condition on the equalizer, this is fixed in (Theorem 1.3, [Marvan's thesis](#MarvanThesis)). The extra condition is that the equalizer must remain an equalizer after an application of the $V$ functor, which maps fibered manifolds to their vertical tangent bundles.)

* {#MarvanThesis} [[Michal Marvan]], thesis, 1989 ([[MarvanThesis.pdf:file]], [web](http://www.slu.cz/math/cz/lide/marvan-michal/docs/mar89-ocr.pdf))

* {#Marvan89} [[Michal Marvan]], _On the horizontal cohomology with general coefficients_, 1989 ([web announcement](http://old.math.slu.cz/People/MichalMarvan/Annotations/horizontal.php), [web archive](http://dml.cz/dmlcz/701469))

* {#Marvan93} [[Michal Marvan]], section 1.1 of _On Zero-Curvature Representations of Partial Differential Equations_,  (1993) ([web](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.5631))

Discussion in [[synthetic differential geometry]]:

* {#Deligne70} [[Pierre Deligne]], _Equations Différentielles à Points Singuliers Réguliers_, 1970

* {#Kock10} [[Anders Kock]], remark 7.3.1 _Synthetic geometry of manifolds_, Cambridge Tracts in Mathematics 180 (2010). ([pdf](http://home.imf.au.dk/kock/SGM-final.pdf))

In the context of [[algebraic geometry]] and [[D-geometry]] the comonad structure is observed in:

* {#Lurie} [[Jacob Lurie]], *Notes on crystals and algebraic $\mathcal{D}$-modules* (2010) [[[Lurie-NotesOnCrystals.pdf:file]]]

Discussion in [[differential cohesion]]:

* [[Igor Khavkine]], [[Urs Schreiber]], _[[schreiber:Synthetic variational calculus|Synthetic geometry of differential equations: I. Jets and comonad structure]]_ ([arXiv:1701.06238](https://arxiv.org/abs/1701.06238))

Discussion in differentially cohesive [[modal homotopy type theory|modal]] [[homotopy type theory]]:

* {#Wellen17} [[Felix Wellen]], _[[schreiber:thesis Wellen|Formalizing Cartan Geometry in Modal Homotopy Type Theory]]_, 2017

For more references see at _[[jet bundle]]_.

[[!redirects jet comonads]]

[[!redirects Jet comonad]]
[[!redirects Jet comonads]]


jet group

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## Idea

The concept of _jet group_ is the generalization of [[general linear group]] from first order to higher order [[jets]].

In terms of [[synthetic differential geometry]]/[[differential cohesion]] a [[general linear group]] is the [[automorphism group]] of a first-order [[infinitesimal disk]], while a jet group is the automorphism group of a higher order infinitesimal disk. See also at _[differential cohesion -- Frame bundles](differential+cohesive+%28infinity%2C1%29-topos#GLnTangentBundles)_.

## Properties

### Homotopy type
 {#HomotopyType}

For all $k \in \mathbb{N}$, the [[homotopy type]] of the orientation preserving jet group $GL^k_p(n)$ is that of the ordinary orientation-preserving [[general linear group]] $GL(n)$, and the canonical projection

$$
  GL^k_+(n) \longrightarrow GL_+(n)
$$

is, on the level of the underlying [[topological spaces]], a [[homotopy equivalence]], indeed it preserves the [[maximal compact subgroup]], which is the [[special orthogonal group]] $SO(n)$ on both sides

(see [Kolář, Michor & Slovák 1993, §13.1 & Prop. on p. 131](#KolářMichorSlovák93); [Dartnell 1994, section 1](#Dartnell94), also [Grasseau 2006, pp. 14](#Grasseau06)).

### Group homology

The canonical projection $GL^k_+(n) \longrightarrow GL_+(n)$ also induces an [[isomorphism]] on  [[group homology]] with constant [[integer]] coefficients

$$
  H_\bullet^{grp}(GL^k_+(n), \mathbb{Z})
  \stackrel{\simeq}{\longrightarrow}
  H_\bullet^{grp}(GL_+(n),\mathbb{Z})
  \,.
$$

([Dartnell 94, theorem 1.1](#Dartnell94))

## Related concepts

* [[higher order frame bundle]]

* [[jet groupoid]]

## References

Original discussion in the context of [[integrability of G-structures]]

* {#Guillemin65} [[Victor Guillemin]], section 3 of: *The integrability problem for $G$-structures*, Trans. Amer. Math. Soc. **116** (1965), 544-560 [[jstor:1994134](http://www.jstor.org/stable/1994134)]

and in the context of [[natural vector bundles]]:

* {#Terng78} [[Chuu-Lian Terng]], p. 779 of: *Natural vector bundles and natural differential operators*, Amer. J. Math. **100** (1978) 775-828 [[doi:10.2307/2373910](https://doi.org/10.2307/2373910), [jstor:2373910](https://www.jstor.org/stable/2373910)]

Textbook accounts and lecture notes:

* [[Demeter Krupka]], [[Josef Janyška]], §2.2 in: _Lectures on differential invariants_, Univerzita J. E. Purkyně, Brno (1990) [ISBN:80-210-165-8, [researchgate](https://www.researchgate.net/publication/36792711_Lectures_on_Differential_Invariants)]

  > (there jet groups are called "differential groups")

* {#KolářMichorSlovák93} [[Ivan Kolář]], [[Peter Michor]], [[Jan Slovák]], section 13 of: *[[Natural operators in differential geometry]]*, Springer (1993)  [[doi:10.1007/978-3-662-02950-3](https://link.springer.com/book/10.1007/978-3-662-02950-3), [book webpage](https://www.emis.de/monographs/KSM/), [pdf](http://www.emis.de/monographs/KSM/kmsbookh.pdf)]

See also

* Wikipedia, _[Jet group](https://en.wikipedia.org/wiki/Jet_group)_

* [MO discussion](http://mathoverflow.net/a/55322/381)

Discussion of the [[group cohomology|group]] [[homology]] of jet groups:

* {#Dartnell94} [[Pablo Dartnell]], *On the homology of groups of jets*, Journal of Pure and Applied Algebra **92** 2 (1994) 109-121 [doi:10.1016/0022-4049(94)90017-5]

* [[Emmanuel Dror Farjoun]], Jekel, Suciu, _Homology of jet groups_ ([pdf](http://www.northeastern.edu/suciu/papers/jets.pdf))

Discussion of jet-[[frame bundles]] and their [[Cartan geometry]]:

* {#Grasseau06} Michael Grasseau, *Jets, frames, and their Cartan geometry* [[arXiv:math-ph/0603063](https://arxiv.org/abs/math-ph/0603063), [hal:00021276](https://hal.science/hal-00021276)]

[[!redirects jet groups]]

[[!redirects group of jets]]
[[!redirects groups of jets]]


jet groupoid

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## Idea

Given a [[smooth manifold]] $X$, and given $k \in \mathbb{N}\cup \{\infty\}$, there is a [[Lie groupoid]] whose [[objects]] are the points of $X$ and whose [[morphisms]] between two such points $x\to y$ are order-$k$ [[jets]] of local [[diffeomorphisms]] taking $x$ to $y$.

The [[automorphism groups]] of objects in these groupoids are _[[jet groups]]_.

Hence these Lie groupoids are often called _jet groupoids_, e.g. ([Lorenz 09](#Lorenz09)). If one passes from jets to [[germs]] of local diffeomorphisms then one arrives essentially at the [[Haefliger groupoid]] of $X$ (except that this has a more discrete smooth structure on its set of morphisms).

In a context of [[synthetic differential geometry]] or [[differential cohesion]] there is the bundle $T_{inf}^k X\to X$ of order-$k$ [[infinitesimal neighbourhoods]] in $X$. In terms of this the jet groupoid is the [[Atiyah groupoid]] of $T_{inf}^k X$, the groupoid whose morphisms between objects $x$ and $y$ are isomorphism of the [[fibers]] of this bundle over these points.

## Related concepts

* [[jet bundle]]

## References

* {#Lorenz09} Arne Lorenz, _Jet Groupoids, Natural Bundles
and the Vessiot Equivalence Method_, Thesis ([pdf](http://wwwb.math.rwth-aachen.de/~arne/Dissertation_Lorenz_Arne.pdf)) 2009

[[!redirects jet groupoids]]


Jet Nestruev

textbook on [[differential geometry]]:

* _Smooth manifolds and Observables_, Graduate texts in mathematics 218, 2003

## related $n$Lab entries

* [[smooth manifold]]

* [[smooth Serre-Swan theorem]]

category: people


jet prolongation

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## Definition

For $E \to X$ a [[bundle]] of [[smooth manifolds]], then the _jet prolongation_ is the map that sends a [[section]] $\sigma$ of $E$ to its [[jet]], hence the section of the [[jet bundle]] $j^\ast E \to X$ which is defined by all the finite [[partial derivatives]] of $\sigma$.

## Related concepts

* [[local Lagrangian]]

[[!redirects jet prolongations]]

[[!redirects jet prolongation map]]
[[!redirects jet prolongation maps]]


jet scheme

## Idea and definition

For finite $m$ this is a version of $m$-[[jet space]] in [[algebraic geometry]].

Let $k$ be the algebraically closed field, $Sch/k$ the category of schemes over $k$ and $X$ an object in $Sch/k$. The presheaf
$$
(Sch/k)^{op}\to Set\,\,\,\,\,\,\,\,\,\,
 Y\mapsto (Sch/k) (Y\times_k k[t]/t^{m+1},X)
$$
is representable by a $k$-scheme of finite type $X_m$ the $m$-jet scheme.

An analogue of the $\infty$-jet space is the [[arc space]].

## References

Readable introduction is in

* M. Popa, 571 Ch. 5. _Jet schemes and arc spaces_, [pdf](https://people.math.harvard.edu/~mpopa/571/chapter5.pdf)

* [[A. Beilinson]], [[V. Drinfeld]], [[Chiral Algebras]]

* L. Ein, M. Mustaţǎ, _Jet schemes and singularities_, Algebraic geometry-
Seattle 2005, 505–546, Proc. Sympos. Pure Math. 80, Part 2, Amer. Math. Soc.,
Providence, RI, 2009 [MR2483946](http://www.ams.org/mathscinet-getitem?mr=2483946)
* L Ein, M Mustaţǎ, T Yasuda, _Jet schemes, log discrepancies and inversion of adjunction_, Invent. Math., 153 (2003) 519–535 [math.AG/0209392](http://arxiv.org/abs/math/0209392)
* M Mustaţǎ, _Jet schemes of locally complete intersection canonical singularities_, with an appendix by David Eisenbud and Edward Frenkel, Invent. Math., 145 (2001) 397–424; _Singularities of pairs via jet schemes_, J. Amer. Math. Soc., 15 (2002) 599–615

[[!redirects jet schemes]]


jet space

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# Jet spaces
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## Idea

The notion of jet space or _[[jet bundle]]_ is a generalization of the notion of [[tangent space]]s and [[tangent bundle]]s, respectively. While a tangent [[vector]] is an [[equivalence class]] of [[germ]]s of [[curve]]s with order-$1$ tangency at a given point in the target, jet spaces are equivalence classes of [[germ]]s of [[smooth map]]s with respect to (finite) order-$k$ tangency at some point in the target.

One version in algebraic geometry is [[jet scheme]].

From the [[nPOV]], the map from a bundle to its jet bundle can be understood in terms of the [[jet comonad]].

## Related pages

* [[jet group]], [[jet groupoid]]

* [[jet bundle]]

* [[metric jet]]

* [[h-principle]]

* in [[algebraic geometry]]: [[jet scheme]]
* ín [[arithmetic geometry]]: [[arithmetic jet space]]

## References

Jet bundles were first introduced by [[Charles Ehresmann]].

* wikipedia: [jet](http://en.wikipedia.org/wiki/Jet_%28mathematics%29), [jet bundle](http://en.wikipedia.org/wiki/Jet_bundle)

* Ivan Kolar, [[Jan Slovak]], [[Peter Michor]], _Natural operations in differential geometry_, book 1993, 1999, [pdf](http://www.emis.de/monographs/KSM/kmsbookh.pdf), hyper-[dvi](http://www.emis.de/monographs/KSM/kmsbookh.dvi.gz), [ps](http://www.emis.de/monographs/KSM/kmsbookh.ps.gz)

* G. Sardanashvily, _Fibre bundles, jet manifolds and Lagrangian theory_,  Lectures for theoreticians, [arXiv:0908.1886](http://xxx.lanl.gov/abs/0908.1886)

* D. J. Saunders, _The geometry of jet bundles_, London Mathematical Society Lecture Note Series __142__, Cambridge Univ. Press 1989.

* Arthemy Kiselev, _The twelve lectures in the (non)commutative geometry of differential equations_, preprint IHES M/12/13 [pdf](http://preprints.ihes.fr/2012/M/M-12-13.pdf)

#### In the language of schemes

* R. Moosa, T. Scanlon, _Jet and prolongation spaces_, J. Inst. Math. Jussieu 9(02) 391 (2010) [doi](https://doi.org/10.1017/s1474748010000010)
* Shihoko Ishii, _Jet schemes, arc spaces and the Nash problem_, [arXiv:math.AG/0704.3327](http://arXiv.org/abs/0704.3327)

[[!redirects jet space]]
[[!redirects jet spaces]]


Jethro van Ekeren

* [Institute page](https://w3.impa.br/~jethro/index.html)

* [GoogleScholar page](https://scholar.google.com/citations?user=bK5Wn-4AAAAJ&hl=en)

## Selected writings

On [[vertex operator algebras]] as [[coalgebras over a comonad]]:

* [[Jethro van Ekeren]], *A quantum field comonad* [[arXiv:2305.18223](https://arxiv.org/abs/2305.18223)]

category: people


Jian Xin Lu

* [InSpire page](https://inspirehep.net/authors/999690)

## Selected writings

On [[black branes]] and [[solitonic branes]]:

* [[Michael Duff]], [[Ramzi R. Khuri]], [[Jian Xin Lu]], *String and Fivebrane Solitons: Singular or Non-singular?*, Nucl.Phys. B **377** (1992) 281-294 [[arXiv:hep-th/9112023](https://arxiv.org/abs/hep-th/9112023), doi:10.1016/0550-3213(92)90025-7]

* [[Michael Duff]], [[Jian Xin Lu]], *Black and super $p$-branes in diverse dimensions*, Nucl. Phys. B **416** (1994) 301-334 [[arXiv:hep-th/9306052](http://arxiv.org/abs/hep-th/9306052)]

* {#DuffKhuriLu94} [[Mike Duff]], [[Ramzi R. Khuri]], [[Jian Xin Lu]], *String Solitons*, Phys. Rept. **259** (1995) 213-326 [[arXiv:hep-th/9412184](https://arxiv.org/abs/hep-th/9412184), doi:10.1016/0370-1573(95)00002-X]

On [[D-brane]] [[brane intersection|intersections]]:

* {#Lu06} [[Jian Xin Lu]], *$(1 + p)$-Dimensional Open $D(p - 2)$ Brane Theories*, JHEP 0108:049 (2001) [[arXiv:hep-th/0102056](https://arxiv.org/abs/hep-th/0102056), [doi:10.1088/1126-6708/2001/08/049](https://doi.org/10.1088/1126-6708/2001/08/049)]

[[!redirects Jian X. Lu]]

[[!redirects J. X. Lu]]


Jiang-Hua Lu

__Jiang-Hua Lu__ is a geometer at the University of Hong Kong. Her PhD is from University of California, Berkeley, advised by [[Alan Weinstein]]. Her main specialty is  [[Poisson geometry]].

She introduced the notion of an [[associative bialgebroid]] over a noncommutative base, and a rather nonsymmetric version of the notion of [[Hopf algebroid]], partly motivated by imagining Poisson groupoids appearing in their quasiclassical limit.

## Selected works

* Jiang-Hua Lu, _Hopf algebroids and quantum groupoids_, Int. J. Math. __7__, 1 (1996) pp. 47-70, [q-alg/9505024](https://arxiv.org/abs/q-alg/9505024), [MR95e:16037](https://mathscinet.ams.org/mathscinet-getitem?mr=95e:16037), [doi](https://doi.org/10.1142/S0129167X96000050)
* Jiang-Hua Lu, _On the Drinfeld double and the [[Heisenberg double]] of a Hopf algebra_, Duke Math. J. __7__:3 (1994) 763-776, [MR1277953](https://www.ams.org/mathscinet-getitem?mr=1277953), [doi](https://doi.org/10.1215/S0012-7094-94-07428-0)

category: people

[[!redirects J-H. Lu]]


Jiannis K. Pachos

* [Institute page](https://theory.leeds.ac.uk/jiannis-pachos/)

* [GoogleScholar page](https://scholar.google.com/citations?user=V0OUoHQAAAAJ&hl=en)

## Selected writings

On [[adiabatic quantum computation]] with [[Berry phase]]-[[quantum gates]] ([[holonomic quantum computation]]):

* [[Jiannis Pachos]], [[Paolo Zanardi]], [[Mario Rasetti]], *Non-Abelian Berry connections for quantum computation*, Phys. Rev. A **61** (2000) 010305 [[arXiv:quant-ph/9907103](https://arxiv.org/abs/quant-ph/9907103), [doi:10.1103/PhysRevA.61.010305](https://doi.org/10.1103/PhysRevA.61.010305)]

* [[Jiannis Pachos]], [[Paolo Zanardi]], *Quantum Holonomies for Quantum Computing*, Int. J. Mod. Phys. B **15** (2001) 1257-1286 [[arXiv:quant-ph/0007110](https://arxiv.org/abs/quant-ph/0007110), [doi:10.1142/S0217979201004836](https://doi.org/10.1142/S0217979201004836)]

On [[topological quantum computation]] by [[braiding]] of [[anyon]] [[worldlines]]:

* [[Gavin K. Brennen]], [[Jiannis K. Pachos]], *Why should anyone care about computing with anyons?*, Proc. R. Soc. A **464** (2008) 1-24 $[$[arXiv:0704.2241](https://arxiv.org/abs/0704.2241), [doi:10.1098/rspa.2007.0026](https://doi.org/10.1098/rspa.2007.0026)$]$

* [[Jiannis K. Pachos]], *Introduction to Topological Quantum Computation*, Cambridge University Press (2012) $[$[doi:10.1017/CBO9780511792908]( https://doi.org/10.1017/CBO9780511792908)$]$

* {#LahtinenPachos17} [[Ville Lahtinen]], [[Jiannis K. Pachos]], _A Short Introduction to Topological Quantum Computation_,  SciPost Phys. **3** 021 (2017) [[arXiv:1705.04103](https://arxiv.org/abs/1705.04103), [doi:10.21468/SciPostPhys.3.3.021](https://scipost.org/SciPostPhys.3.3.021)]

and with focus on [[abelian anyons]]:

* [[Jiannis K. Pachos]], *Quantum computation with abelian anyons on the honeycomb lattice*, International Journal of Quantum Information **4** 6 (2006) 947-954 ([arXiv:quant-ph/0511273](https://arxiv.org/abs/quant-ph/0511273))

On simulating [[anyons]]:

* [[Jiannis Pachos]], *Non-abelian topological Berry-phases*, talk at *[[CQTS]]* [(07 Nov 2022)](Center+for+Quantum+and+Topological+Systems#PachosNov2022)  [video: [rec](https://zoom.us/rec/play/FZOBvACSJsDzpqZ0WIf4WItlhF08IxP-vrgrRlfqsWqHFm8LFiiy5JD_7kTu5d1-WldA0oxXXCgjlbAg.S-7IQQf-XfhxNIbG?continueMode=true&iet=wHgMaPo0jUhLbgeLcRNNRn4t5tDEUui0GTZy7IskgfM.AG.2korr3jfgIJd-6R5zSQmb3fYA-lyqwuLti8O9KDQ0vDH8BJ2-bMcnQ1yboWDw8reV-2SKgLjwd0sVdHZWJR43y1ixw0PN4rGqDzSb3jdnroRh3nsq2fYp2s4b7Iavne-LwST3jI59_Y.gBff8xUXVV4VPqWf5kNIpg.gASLSIaf0KVBzA1A&_x_zm_rtaid=MnFZqJMnRzKokesOCUS66w.1667975314563.2bcd3ca7ce0a0ad02b775305bfa3c96f&_x_zm_rhtaid=473)]

category: people

[[!redirects Jiannis Pachos]]


Jie-qiang Wu

* [InSpire page](https://inspirehep.net/authors/1652725)

## Selected writings

On the [[covariant phase space]] for [[boundary field theory]]:

* [[Daniel Harlow]], [[Jie-qiang Wu]], *Covariant phase space with boundaries*,  J. High Energ. Phys. **2020** 146 (2020). [[arXiv:1906.08616](https://arxiv.org/abs/1906.08616), doi:10.1007/JHEP10(2020)146]

category: people


Jim Gates

Sylvester James Gates Jr., known as Jim Gates, works on [[supersymmetry]], [[supergravity]] and [[superstring theory]].

* [Wikipedia entry](http://en.wikipedia.org/wiki/Sylvester_James_Gates)

## selected writings

* {#GatesGrisaruRocekSiegel83} [[Jim Gates]] Jr, [[Marcus Grisaru]], [[Martin Roček]], [[Warren Siegel]], _Superspace, or One thousand and one lessons in supersymmetry_, Front.Phys. 58 (1983) 1-548  (1983) ([arXiv:hep-th/0108200](https://arxiv.org/abs/hep-th/0108200), [spire:195126](inspirehep.net/record/195126))

  (on [[superspace]])

## related $n$Lab entries

* [[4d supergravity]]

* [[parameterized WZW model]]

* [[adinkra]]

category: people

[[!redirects Sylvester James Gates Jr.]]
[[!redirects Sylvester James Gates, Jr.]]
[[!redirects Sylvester James Gates]]
[[!redirects S. James Gates, Jr.]]
[[!redirects S. James Gates Jr.]]


Jim Pivarski

* [webpage](http://www.watson.org/~mccann/)

category: people


Jim Simons

* [Wikipedia entry](http://en.wikipedia.org/wiki/James_Harris_Simons)

## related entries:

* [[Chern-Simons element]]

* [[Chern-Simons theory]]

category: people


Jim Stasheff

* [Jim Stasheff's home page](https://www2.math.upenn.edu/~jds/)

* interview by [[Kathryn Hess]]: [video](https://www.youtube.com
/watch?v=K8kPS6FZBoc&feature=youtu.be)

* John McCleary, _An appreciation of the work of Jim Stasheff_ ([pdf](http://www.math.unc.edu/Faculty/jds/jds.pdf))

## Selected writings

On [[An-spaces|$A_n$-spaces]] and [[A-∞ algebras]]:

* {#Stasheff63a} [[Jim Stasheff]], *Homotopy associativity of H-spaces I*, Trans. Amer. Math. Soc. **108** 2 (1963) 275-292 [[doi:10.2307/1993608](https://doi.org/10.2307/1993608)]

* {#Stasheff63b} [[Jim Stasheff]], *Homotopy associativity of H-spaces II* **108** 2 (1963) 293-312 [[doi:10.2307/1993609](https://doi.org/10.2307/1993609), [doi:10.1090/S0002-9947-1963-0158400-5](https://doi.org/10.1090/S0002-9947-1963-0158400-5)]

On [[characteristic classes]]:

* [[John Milnor]], [[Jim Stasheff]], _Characteristic classes_, Princeton Univ. Press (1974) ([ISBN:9780691081229](https://press.princeton.edu/books/paperback/9780691081229/characteristic-classes-am-76-volume-76), [doi:10.1515/9781400881826](https://doi.org/10.1515/9781400881826), [pdf](https://www.maths.ed.ac.uk/~v1ranick/papers/milnstas.pdf))

On the [[simplicial de Rham complex]] and [[equivariant de Rham cohomology]]:

* {#BottShulmanStasheff76} [[Raoul Bott]], [[Herbert Shulman]], [[Jim Stasheff]], _On the de Rham theory of certain classifying spaces_, Advances in Mathematics, Volume 20, Issue 1, April 1976, Pages 43-56 (doi:10.1016/0001-8708(76)90169-9, [pdf](https://core.ac.uk/download/pdf/82496263.pdf))

On [[dg-Lie algebras]] and [[L-∞ algebras]]:

* {#Stasheff92} [[Jim Stasheff]], _Differential graded Lie algebras, quasi-Hopf algebras and higher homotopy algebras_, in _Quantum groups_ Number 1510 in Lecture Notes in Math. Springer, Berlin, 1992

* {#LadaStasheff92} [[Tom Lada]], [[Jim Stasheff]],  _Introduction to sh Lie algebras for physicists_, Int. J. Theo. Phys. 32 (1993), 1087--1103. ([arXiv:hep-th/9209099](http://arxiv.org/abs/hep-th/9209099))

On [[connections on principal ∞-bundles]]:

* [[Hisham Sati]], [[Urs Schreiber]], [[Jim Stasheff]], _[[schreiber:L-infinity algebra connections|L-∞ algebra connections and applications to String- and Chern-Simons n-transport]]_, in: *Quantum Field Theory*, Birkhäuser (2009) 303-424 ([arXiv:0801.3480](http://arxiv.org/abs/0801.3480), [doi:10.1007/978-3-7643-8736-5_17](https://doi.org/10.1007/978-3-7643-8736-5_17))

* [[Domenico Fiorenza]], [[Urs Schreiber]], [[Jim Stasheff]], _[[schreiber:Cech cocycles for differential characteristic classes]] -- An $\infty$-Lie theoretic construction_, Advances in Theoretical and Mathematical Physics, Volume 16 Issue 1 (2012), pages 149-250 ([arXiv:1011.4735](http://arxiv.org/abs/1011.4735), [euclid:atmp/1358950853](http://projecteuclid.org/euclid.atmp/1358950853))

On [[differential string structures]]:

* {#SSSIII} [[Hisham Sati]], [[Urs Schreiber]], [[Jim Stasheff]], _[[schreiber:Twisted Differential String and Fivebrane Structures]]_, Communications in Mathematical Physics, October 2012, Volume 315, Issue 1, pp 169-213 ([arXiv:0910.4001](http://arxiv.org/abs/0910.4001), [doi:10.1007/s00220-012-1510-3](https://link.springer.com/article/10.1007/s00220-012-1510-3))

On [[homotopy theory]] in [[physics]]:

* Jim Stasheff, _[[A Survey of Cohomological Physics]]_

On [[recognition of relative loop spaces]]:

* {#HLS16} [[Eduardo Hoefel]], [[Muriel Livernet]], [[Jim Stasheff]], _$A_\infty$-actions and recognition of relative loop spaces_, Topology and its Applications **206** (2016) 126-147 [[arXiv:1312.7155](https://arxiv.org/abs/1312.7155), [doi:10.1016/j.topol.2016.03.023](https://doi.org/10.1016/j.topol.2016.03.023)]

A proposal for understanding [[tensor hierarchies]] as [[L-infinity algebra]]-refinenents of [[Leibniz algebras]]:

* [[Sylvain Lavau]], [[Jim Stasheff]], _$L_\infty$-algebra extensions of Leibniz algebras_ ([arXiv:2003.07838](https://arxiv.org/abs/2003.07838))

# Related $n$Lab entries #

* [[associahedron]]

* [[A-infinity-operad]]

* [[A-infinity-category]]

* [[H-space]]

* [[L-infinity algebra]]

* [[simplicial de Rham complex]]

* [[string field theory]]

[[!redirects Stasheff]]
[[!redirects James Stasheff]]
[[!redirects James D. Stasheff]]
[[!redirects James Dillon Stasheff]]
[[!redirects jim stasheff]]
[[!redirects jim_stasheff]]

category: people


jim stasheff > history

< [[jim stasheff]]
[[!redirects jim stasheff - history]]
[[!redirects jim stasheff -- history]]


Jimmie Lawson

* [webpage](https://www.math.lsu.edu/~lawson/)

## Selected writings

On [[cartesian closed category|cartesian closed]] [[convenient categories of topological spaces]], such as [[compactly generated topological spaces]]:

* {#EscardoLawsonSimpson04} [[Martín Escardó]], [[Jimmie Lawson]], [[Alex Simpson]], *Comparing Cartesian closed categories of (core) compactly generated spaces*, Topology and its Applications Volume 143, Issues 1–3, 28 August 2004, Pages 105-145 ([doi:10.1016/j.topol.2004.02.011](https://doi.org/10.1016/j.topol.2004.02.011))

category: people


Jin Chen

* [Orcid page](https://orcid.org/0000-0002-1462-6667)

## Selected writings

On [[KK-compactification]] of [[D=6 N=(1,0) SCFT]] on [[Riemann surfaces]] [[4d superconformal gauge field theory]]:

* [[Jin Chen]], [[Babak Haghighat]], [[Shuwei Liu]], [[Marcus Sperling]], _4d $\mathcal{N}=1$ from 6d D-type $\mathcal{N}=(1,0)$_,  J. High Energ. Phys. **2020** 152 (2020) [[arXiv:1907.00536](https://arxiv.org/abs/1907.00536), doi:10.1007/JHEP01(2020)152]

On [[quantum Seiberg-Witten curves]] in relation to [[class S-theories]] and "[[M3]]"-[[defect branes]] inside [[M5-branes]]:

* [[Jin Chen]], [[Babak Haghighat]], [[Hee-Cheol Kim]], [[Marcus Sperling]], *Elliptic Quantum Curves of Class $\mathcal{S}_k$*,  J. High Energ. Phys. **2021** 28 (2021) [[arXiv:2008.05155](https://arxiv.org/abs/2008.05155), doi:10.1007/JHEP03(2021)028]

On [[quantum Seiberg-Witten curves]] of [[E-string]]-theories in relation to [[D6-D8-brane bound states]]:

* [[Jin Chen]], [[Babak Haghighat]], [[Hee-Cheol Kim]], [[Marcus Sperling]], [[Xin Wang]], *E-string Quantum Curve*, Nuclear Physics B **973** (2021) 115602 [[arXiv:2103.16996](https://arxiv.org/abs/2103.16996), [doi:10.1016/j.nuclphysb.2021.115602](https://doi.org/10.1016/j.nuclphysb.2021.115602)]

On [[QFT with defects|defects]] in the [[KK-compactification]] of the [[D=6 N=(2,0) SCFT]] on [[4-manifolds]]:

* [[Jin Chen]], [[Wei Cui]], [[Babak Haghighat]], [[Yi-Nan Wang]], *SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds*, JHEP **2023** 208 (2023) [[arXiv:2305.09734](https://arxiv.org/abs/2305.09734), doi:10.1007/JHEP11(2023)208]

category: people


Jinwei Yang

* [institute page](https://gauss.math.yale.edu/~jy534/)

* [GoogleScholar page](https://scholar.google.com/citations?user=IZHHrxQAAAAJ&hl=en)

## Selected writings

On [[braided fusion categories]] formed by [[affine Lie algebra]]-[[representations]] at admissible fractional [[level (Chern-Simons theory)|level]]:

* [[Thomas Creutzig]], [[Yi-Zhi Huang]], [[Jinwei Yang]], *Braided tensor categories of admissible modules for affine Lie algebras*, Commun. Math. Phys. **362** (2018) 827–854 [[arXiv:1709.01865](https://arxiv.org/abs/1709.01865)]

category: people


Jiri Dadok

* [webpage](http://www.math.indiana.edu/people/profile.phtml?id=dadok)

## related $n$Lab entries

* [[calibrated geometry]]

category: people


Jiri Vanzura

* [Oberwolfach photo](http://owpdb.mfo.de/person_detail?id=8863)

## related $n$Lab entries

* [[generalized smooth algebra|C∞-ring]]

category: people

[[!redirects Ji?i Vanzura]]


Jiří Adámek

Jiří Adámek is a pure [[category theory|category theorist]]. One of his major contributions, jointly with [[Jiří Rosický]], is the development of the theory of [[Locally Presentable and Accessible Categories]]. He is a student of [[Věra Trnková]].

* [website](https://math.feld.cvut.cz/adamek/)

* [website](https://www.tcs.cs.tu-bs.de/group/adamek/home.html)

* [old website](https://web.archive.org/web/20180819015939/https://www.tu-braunschweig.de/iti/mitarbeiter/adamek/)

## Selected writings

On [[automata]] via tools from [[category theory]]:

* [[Jiří Adámek]], *Free algebras and automata realizations in the language of categories*, Commentationes Mathematicae Universitatis Carolinae **15**.4 (1974) 589-602 [[eudml:16649](https://eudml.org/doc/16649)]

* [[Jiří Adámek]], Věra Trnková, *Automata and algebras in categories* **37** Springer (1990) [[ISBN:9780792300106](https://link.springer.com/book/9780792300106)]

On [[Scott-complete categories]]:

* [[Jiří Adámek]], *A categorical generalization of Scott domains*, Mathematical Structures in Computer Science **7** 5  (1997) 419 - 443 [[doi:10.1017/S0960129597002351](https://doi.org/10.1017/S0960129597002351)]

On [[category theory]] with emphasis on [[concrete categories]]:

* [[Jiri Adamek|Jiří Adámek]], [[Horst Herrlich]], [[George Strecker]], *[[Abstract and Concrete Categories -- The Joy of Cats]]*, John Wiley and Sons, New York (1990), reprinted in: Reprints in Theory and Applications of Categories **17** (2006) 1-507 ([tac:tr17](http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html), [webpage](http://katmat.math.uni-bremen.de/acc/), [pdf](http://katmat.math.uni-bremen.de/acc/acc.pdf))

On [[locally presentable categories|locally presentable]] and [[accessible categories]]:

* {#AdamekRosicky} [[Jiří Adámek]], [[Jiří Rosický]], _[[Locally presentable and accessible categories]]_, London Mathematical Society Lecture Note Series **189**, Cambridge University Press 1994 ([doi:10.1017/CBO9780511600579](https://doi.org/10.1017/CBO9780511600579))

On [[accessible categories]] via [[doctrines of limits]]:

* {#AdámekBorceuxLackRosicky2002} [[Jiří Adámek]], [[Francis Borceux]], [[Stephen Lack]], [[Jiri Rosicky]], *A classification of accessible categories*, Journal of Pure and Applied Algebra **175** 1–3 (2002)  7-30 [doi:10.1016/S0022-4049(02)00126-3]

On [[coalgebras over endofunctors]]:

* [[Jiří Adámek]], _Introduction to Coalgebra_, Theory and Applications of Categories **14** 8 (2005) 157-199 [[tac:14-8](http://www.tac.mta.ca/tac/volumes/14/8/14-08abs.html), [pdf](http://www.tac.mta.ca/tac/volumes/14/8/14-08.pdf)]

On [[algebraic theories]]:

* [[Jiří Adámek]], [[Jiří Rosický]], [[Enrico Vitale]], *Algebraic theories*, Cambridge University Press (2011) [[doi:10.1017/CBO9780511760754](https://doi.org/10.1017/CBO9780511760754), [pdf](https://perso.uclouvain.be/enrico.vitale/gab_CUP2.pdf)]

## Related entries

* [[Adámek's fixed point theorem]]

* [[Locally Presentable and Accessible Categories]]

* [[The Joy of Cats]]

category: people

[[!redirects Jiří Adámek]]
[[!redirects Jiri Adamek]]
[[!redirects Jiřı́ Adámek]]
[[!redirects Jirí Adámek]]

[[!redirects Adamek]]
[[!redirects Adámek]]


Jiří Chýla

[[!redirects Jiri Chyla]]

* [webpage](https://www.fzu.cz/~chyla/)

## Selected writings

On the [[quark]]-model and [[quantum chromodynamics]]:

* [[Jiri Chyla]], _Quarks, partons and Quantum Chromodynamics_, ([spire:674163/)](http://inspirehep.net/record/674163/), [[ChylaQuarksQCD.pdf:file]])

category: people


Jiří Matoušek

* Wikipedia entry

## Selected writings

Discussion of [[homotopy groups]] in [[computational topology]]:

* [[Martin Čadek]], [[Marek Krčál]], [[Jiří Matoušek]], [[Lukáš Vokřínek]], [[Uli Wagner]], _Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension_, SIAM J. Comput., 43(5), 1728–1780  ([arXiv:1211.3093](https://arxiv.org/abs/1211.3093), [doi:10.1137/120899029](https://doi.org/10.1137/120899029))

* [[Martin Čadek]], [[Marek Krčál]], [[Jiří Matoušek]], [[Lukáš Vokřínek]], [[Uli Wagner]], _Extendability of continuous maps is undecidable_, Discrete Comput Geom (2014) 51: 24 ([arXiv:1302.2370](https://arxiv.org/abs/1302.2370), [doi:10.1007/s00454-013-9551-8](https://doi.org/10.1007/s00454-013-9551-8))

Discussion of [[Cohomotopy]]-sets in [[computational topology]]:

* [[Martin Čadek]], [[Marek Krčál]], [[Jiří Matoušek]], [[Francis Sergeraert]], [[Lukáš Vokřínek]], [[Uli Wagner]], _Computing all maps into a sphere_, Journal of the ACM, Volume 61 Issue 3, May 2014 Article No. 1 ([arxiv:1105.6257](https://arxiv.org/abs/1105.6257))

category: people

[[!redirects J Matoušek]]
[[!redirects Jiri Matousek]]


Jiří Nárožný

* [institute page](https://www.mff.cuni.cz/en/faculty/organizational-structure/people?hdl=11706)

## Selected writings

On [[higher gauge theory]]:

* [[Leron Borsten]], [[Mehran Jalali Farahani]], [[Branislav Jurčo]], [[Hyungrok Kim]], [[Jiří Nárožný]], [[Dominik Rist]], [[Christian Saemann]], [[Martin Wolf]], *Higher Gauge Theory*, in *[[Encyclopedia of Mathematical Physics 2nd ed]]*, Elsevier (2024) [[arXiv:2401.05275](https://arxiv.org/abs/2401.05275)]

category: people

[[!redirects Jiri Narozny]]


Jiří Rosický

Jiří Rosický is a pure [[category theory|category theorist]]. One of his major contributions, jointly with [[Jiří Adámek]], is the development of the theory of [[Locally Presentable and Accessible Categories]].

* [website](http://www.math.muni.cz/~rosicky/)

* [https://en.m.wikipedia.org/wiki/Jiří_Rosický_(mathematician](https://en.m.wikipedia.org/wiki/Jiří_Rosický_(mathematician)

## Selected writings

On [[locally presentable categories|locally presentable]] and [[accessible categories]]:

* {#AdamekRosicky} [[Jiří Adámek]], [[Jiří Rosický]], _[[Locally presentable and accessible categories]]_, London Mathematical Society Lecture Note Series **189**, Cambridge University Press 1994 ([doi:10.1017/CBO9780511600579](https://doi.org/10.1017/CBO9780511600579))

On [[sketches]] (and [[accessible categories]]) the generality of [[enriched category theory]]:

* [[Francis Borceux]], [[Carmen Quinteriro]], [[Jiří Rosický]], *A theory of enriched sketches*, Theory and Applications of Categories, **4** 3 (1998) 47-72 [[tac:4-03](http://www.tac.mta.ca/tac/volumes/1998/n3/4-03abs.html), [pdf](http://www.tac.mta.ca/tac/volumes/1998/n3/n3.pdf)]

On [[accessible categories]] via [[doctrines of limits]]:

* {#AdámekBorceuxLackRosicky2002} [[Jiří Adámek]], [[Francis Borceux]], [[Stephen Lack]], [[Jiri Rosicky]], *A classification of accessible categories*, Journal of Pure and Applied Algebra **175** 1–3 (2002)  7-30 [doi:10.1016/S0022-4049(02)00126-3]

On (co-)[[reflective factorization systems]]:

* {#RosickyTholen08} [[Jiri Rosicky]], [[Walter Tholen]], _Factorization, Fibration and Torsion_, Journal of Homotopy and Related Structures, **2** 2 (2007) 295-314  [[arXiv:0801.0063](http://arxiv.org/abs/0801.0063), [publisher](http://www.emis.de/journals/JHRS/volumes/2007/n2a14/)]

On [[combinatorial model categories]]:

* [[Jiří Rosický]], *On combinatorial model categories*, Appl. Cat. Str. 17 (2009), 303-316 ([arXiv:0708.2185](https://arxiv.org/abs/0708.2185))

On [[convenient categories of topological spaces]] and [[directed homotopy theory]]:

* {#FajstrupRosicky08} [[Lisbeth Fajstrup]], [[Jiří Rosický]], _A convenient category for directed homotopy_, Theory and Applications of Categories, Vol. 21, 2008, No. 1, pp 7-20. ([arXiv:0708.3937](https://arxiv.org/abs/0708.3937), [tac:21-01](http://www.tac.mta.ca/tac/volumes/21/1/21-01abs.html))

On [[algebraic theories]]:

* [[Jiří Adámek]], [[Jiří Rosický]], [[Enrico Vitale]], *Algebraic theories*, Cambridge University Press (2011) [[doi:10.1017/CBO9780511760754](https://doi.org/10.1017/CBO9780511760754), [pdf](https://perso.uclouvain.be/enrico.vitale/gab_CUP2.pdf)]

On [[class-locally presentable categories]]:

* [[Boris Chorny]], [[Jiří Rosický]], _Class-locally presentable and class-accessible categories_, Journal of Pure and Applied Algebra **216**, Issue 10 (2012) pp 2113–2125 ([doi:10.1016/j.jpaa.2012.01.015](https://doi.org/10.1016/j.jpaa.2012.01.015))

On [[2-colimits]] of [[accessible categories]] (i.e. in [[AccCat]]):

* [[Robert Paré]], [[Jiří Rosický]], *Colimits of accessible categories*, Math. Proc. Cambr. Phil. Soc. **155** (2013) 47-50 [[doi:10.1017/S0305004113000030](https://doi.org/10.1017/S0305004113000030), [arXiv:1110.0767](http://arxiv.org/abs/1110.0767)]

Introducing [[cellular categories]]:

* {#MakkaiRosický14} [[M. Makkai]], [[J. Rosický]], _Cellular categories_, J. Pure Appl. Alg. **218** (2014) 1652-1664 [[arXiv:1304.7572](https://arxiv.org/abs/1304.7572), [doi:10.1016/j.jpaa.2014.01.005](https://doi.org/10.1016/j.jpaa.2014.01.005)]

## Related entries

* [[locally presentable category]]

* [[accessible category]]

* [[Vopěnka's principle]]

* [[Locally Presentable and Accessible Categories]]

* [[quantale]]

[[!redirects Jiri Rosicky]]
[[!redirects Rosicky]]
[[!redirects J. Rosicky]]
[[!redirects Jiří Rosicky]]
[[!redirects J. Rosický]]
[[!redirects Jiří Rosický]]

[[!redirects Jiři Rosický]]

category: people


Jiří Vanžura

* [webpage](https://www.muni.cz/en/people/28787-jiri-vanzura)

* [webpage](http://www.math.cas.cz/homepage/main_page.php?id_membre=74)

## selected writings

* {#CadekVanzura92} [[Martin Čadek]], [[Jiří Vanžura]], _On oriented vector bundles over CW-complexes of dimension 6 and 7_, Comment. Math. Univ. Carolin. 33,4(1992)727–736 ([pdf](http://emis.impa.br/EMIS/journals/CMUC/pdf/cmuc9204/cadek.pdf))

* {#CadekVanzura93} [[Martin Čadek]], [[Jiří Vanžura]], _On the classification of oriented vector bundles over 5-complexes_, Czechoslovak Mathematical Journal, Vol. 43 (1993), No. 4, 753–764 ([dml:128427](https://dml.cz/handle/10338.dmlcz/128427))

* {#CadekVanzura95} [[Martin Čadek]], [[Jiří Vanžura]], _On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes_, Commentationes Mathematicae Universitatis Carolinae, vol. 36 (1995), issue 2, pp. 377-394 ([dml-cz:118764](https://dml.cz/handle/10338.dmlcz/118764))

* {#CadekVanzura97} [[Martin Čadek]], [[Jiří Vanžura]], _On $Sp(2)$ and $Sp(2) \cdot Sp(1)$-structures  in 8-dimensional vector bundles_, Publicacions Matemàtiques Vol. 41, No. 2 (1997), pp. 383-401 ([jstor:43737249](https://www.jstor.org/stable/43737249))

* {#CadekVanzura98a} [[Martin Čadek]], [[Jiří Vanžura]], _On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes_,  Colloquium Mathematicum (1998), 76 (2), pp 213-228 ([web](http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-cmv76z2p213bwm))

* {#CadekVanzura98b} [[Martin Čadek]], [[Jiří Vanžura]], _Almost quaternionic structures on eight-manifolds_, Osaka J. Math. Volume 35, Number 1 (1998), 165-190 ([euclid:1200787905](https://projecteuclid.org/euclid.ojm/1200787905))

* {#CadekVanzura98c} [[Martin Čadek]], [[Jiří Vanžura]], _Various structures in 8-dimensional vector bundles over 8-manifolds_, Banach Center Publications (1998) Volume: 45, Issue: 1, page 183-197 ([dml:208903](https://eudml.org/doc/208903))

* {#CadekCrabbVanzura08} [[Martin Čadek]], Michael Crabb, [[Jiří Vanžura]],  _Obstruction theory on 8-manifolds_, manuscripta math. 127 (2008), 167-186 ([arXiv:0710.0734](https://arxiv.org/abs/0710.0734))

* {#CadekCrabbVanzura10} [[Martin Čadek]], Michael Crabb, [[Jiří Vanžura]], _Quaternionic structures_, Topology and its Applications Volume 157, Issue 18, 1 December (2010), Pages 2850-2863 ([doi:10.1016/j.topol.2010.09.005](https://doi.org/10.1016/j.topol.2010.09.005))

## related $n$Lab entries

* [[5-manifold]], [[8-manifold]]

* [[G-structure]]

* [[quaternion-Kähler manifold]]

* [[Sp(n).Sp(1)]]

* [[Spin(4)]], [[Spin(5)]], [[Spin(8)]]

* [[triality]]

* [[quaternion-Kähler manifold]]

* [[Euler class]]

category: people

[[!redirects Jiri Vanzura]]


Jiří Wiedermann

* [personal page](https://www.cs.cas.cz/wieder/)

* [institute page](https://www.avcr.cz/en/about-us/cas-structure/council-for-sciences/list-of-members-of-council-for-sciences/prof-RNDr-Jiri-Wiedermann-DrSc/)

* [list](https://webspace.science.uu.nl/~leeuw112/list-vLW.html) of joint writings with [[Jan van Leeuwen]]

## Selected writings

On [[computation]]:

* {#vanLeeuwenWiedermann15} [[Jan van Leeuwen]], [[Jiří Wiedermann]]: *What is Computation -- An Epistemic Approach*, p. 1-13 in Proceedings of *[SOFSEM 2015](http://www.sofsem.cz/sofsem15/): Theory and Practice of Computer Science*, Lecture Notes in Computer Science **8939**, Springer (2015) [[pdf:10.1007/978-3-662-46078-8](https://doi.org/10.1007/978-3-662-46078-8), talk slides: [pdf](http://www.sofsem.cz/sofsem15/files/presentations/invited/vanLeeuwenWiedermann.pdf)]

* {#vanLeeuwenWiedermann17} [[Jan van Leeuwen]], [[Jiří Wiedermann]]: *Knowledge, Representation and the Dynamics of Computation*, pp. 69-89 in: *Representation and Reality in Humans, Other Living Organisms and Intelligent Machines*, Studies in Applied Philosophy, Epistemology and Rational Ethics **28**, Springer (2017) [[doi:10.1007/978-3-319-43784-2_5](https://doi.org/10.1007/978-3-319-43784-2_5), [[LeeuwenWiedermann-Computation.pdf:file]]]

\begin{imagefromfile}
    "file_name": "LeeuwenWiedermann-Computation.jpg",
    "width": 570,
    "unit": "px",
    "margin": {
        "top": -40,
        "bottom": 20,
        "right": 0,
        "left": 10
    },
    "caption": "(from [van Leeuwen and Wiedermann 2017](#vanLeeuwenWiedermann17))"
\end{imagefromfile}

* {#vanLeeuwenWiedermann19} [[Jan van Leeuwen]], [[Jiří Wiedermann]], *Understanding Computation -- A General Theory of Computational Processes*, Technical Report UU-CS-2019-012, Utrecht University (2019) [[dspace:1874/390075](https://dspace.library.uu.nl/handle/1874/390075), [pdf](http://www.cs.uu.nl/research/techreps/repo/CS-2019/2019-012.pdf), [pdf](https://dspace.library.uu.nl/bitstream/handle/1874/390075/2019_012.pdf?sequence=1&isAllowed=y)]

category: people

[[!redirects Jiri Wiedermann]]


JM

I just saw that it said "possibly Jonas Meyer" for "JM" on the Contributors in nLab page, and I wanted to say that I am Jonas Meyer and I have not contributed anything on nLab under "JM".  (Perhaps JM is also named Jonas Meyer, but I doubt it.)  I hope it is appropriate to post this here.


Joachim Cuntz

__Joachim Cuntz__ is a mathematician at Münster, Germany. His central interests include [[functional analysis]], [[operator algebras]], [[homological algebra]] (especially [[cyclic homology]]) and [[noncommutative geometry]]. He also studied regularity and smoothness conditions in ring theory.

* [webpage](http://wwwmath.uni-muenster.de/u/cuntz/cuntz.html)
* wikipedia [de](http://de.wikipedia.org/wiki/Joachim_Cuntz)
* J. Cuntz, _Dimension function on simple $C^\ast$-algebras_, [pdf](http://wwwmath.uni-muenster.de/u/cuntz/cuntz.pdf)
* J. Cuntz, [[D. Quillen]], _Algebra extensions and nonsingularity_, J. Amer. Math. Soc. __8__  (1995),  no. 2, 251–289, [MR96c:19002](http://www.ams.org/mathscinet-getitem?mr=1303029), [doi](http://ams.mpim-bonn.mpg.de/leavingmsn?url=http://dx.doi.org/10.2307/2152819); _Cyclic homology and nonsingularity_,  J. Amer. Math. Soc. __8__  (1995),  no. 2, 373–442, [MR96e:19004](http://www.ams.org/mathscinet-getitem?mr=1303030), [doi](http://dx.doi.org/10.2307/2152822)

[[!redirects J. Cuntz]]


Joachim Gomis

* [webpage](http://icc.ub.edu/~gomis/)

## related $n$Lab entries

* [[supergravity]]

category: people


Joachim Hilgert

* [Institute page](https://www.uni-paderborn.de/person/220)

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=30575)

## Selected writings

On [[Lie theory]]

on [[Lie semigroups]]:

* [[Joachim Hilgert]], [[Karl-Hermann Neeb]], *Lie Semigroups and their Applications*. Lecture Notes in Mathematics **1552**, Springer 1993 ([doi:10.1007/BFb0084640](https://link.springer.com/book/10.1007/BFb0084640))

on [[Lie groups]];

* {#HilgertNeeb12} [[Joachim Hilgert]], [[Karl-Hermann Neeb]], _Structure and Geometry of Lie Groups_, Springer Monographs in Mathematics, Springer-Verlag New York, 2012 ([doi:10.1007/978-0-387-84794-8](https://link.springer.com/book/10.1007/978-0-387-84794-8))

category: people


Joachim Kock

* [website](http://www.mat.uab.es/~kock/)

* [Copenhagen website](https://www.math.ku.dk/english/about/news/new-names/joachim-kock-associate-professor/)

## Selected writings

On [[Frobenius algebras]] and [[2d TQFT|2d]] [[topological quantum field theory]]:

* {#Kock2004} [[Joachim Kock]], *Frobenius Algebras and 2d Topological Quantum Field Theories*, Cambridge U. Press (2004) [[doi:10.1017/CBO9780511615443](https://doi.org/10.1017/CBO9780511615443), [webpage](http://mat.uab.cat/~kock/TQFT.html), [course notes pdf](http://mat.uab.es/~kock/TQFT/FS.pdf), [[Kock-FrobAlgTQFT-short.pdf:file]]]

On [[quantum cohomology]]:

* [[Joachim Kock]], [[Israel Vainsencher]], *An Invitation to Quantum Cohomology -- Kontsevich's Formula for Rational Plane Curves*, Birkhäser (2007) [[doi:10.1007/978-0-8176-4495-6](https://doi.org/10.1007/978-0-8176-4495-6)]

Proving the [[biequivalence]] between [[Feynman categories]] and [[colored operads]]:

* {#BataninKockWeber15} [[Michael Batanin]], [[Joachim Kock]], [[Mark Weber]], _Regular patterns, substitudes, Feynman categories and operads_, Theory Appl. Categ. 33 (2018), 148--192 ([arXiv:1510.08934](https://arxiv.org/abs/1510.08934))

* {#GKT18} [[Imma Gálvez-Carrillo]], [[Joachim Kock]],  [[Andrew Tonks]], _Homotopy linear algebra_. Proc. Roy. Soc. Edinburgh Sect. A, 148(2):293–325, 2018 ([arXiv:1602.05082](https://arxiv.org/abs/1602.05082)).

* [[Imma Gálvez-Carrillo]], [[Joachim Kock]], [[Andrew Tonks]], _Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees_. Adv. Math., 254:79–117, 2014.

* {#GHK} [[David Gepner]], [[Rune Haugseng]], [[Joachim Kock]], _∞-Operads as analytic monads_, ([arXiv:1712.06469](https://arxiv.org/abs/1712.06469))

* [[Imma Gálvez-Carrillo]], Joachim Kock, [[Andrew Tonks]], _Decomposition spaces, incidence algebras and Möbius inversion_, [arXiv:1404.3202](https://arxiv.org/abs/1404.3202)

* Nicolas Behr, Joachim Kock, _Tracelet Hopf algebras and decomposition spaces_, [arXiv:2105.06186](https://arxiv.org/abs/2105.06186)

> Tracelets are the intrinsic carriers of causal information in categorical [[rewriting system]]s. In this work, we assemble tracelets into a symmetric monoidal decomposition space, inducing a cocommutative Hopf algebra of tracelets. This Hopf algebra captures important combinatorial and algebraic aspects of rewriting theory, and is motivated by applications of its representation theory to stochastic rewriting systems such as chemical reaction networks.

category: people

[[!redirects J. Kock]]


Joachim Lambek

Joachim Lambek, (1922-2014), usually called Jim, was a mathematician, logician, theoretical linguist, ..., based at McGill university.

* [wikipedia page](http://en.wikipedia.org/wiki/Joachim_Lambek)

* [index of his writing since 2000](http://www.math.mcgill.ca/barr/lambek/pdffiles/)

## Selected writings

Suggesting [[enriched category|enrichment]] in [[multicategories]]:

* [[Joachim Lambek]], *Deductive Systems and Categories II: Standard constructions and closed categories*,  In: [[Peter Hilton]] (eds.) *Category Theory, Homology Theory and their Applications I*, Lecture Notes in Mathematics **86** Springer 1969 ([doi:10.1007/BFb0079385](https://doi.org/10.1007/BFb0079385), [pdf](https://link.springer.com/content/pdf/10.1007/BFb0079385.pdf))

On the role of [[adjunctions]] and [[dualities]] in [[mathematics]]:

* {#Lambek} [[Joachim Lambek]], _The Influence of Heraclitus on Modern Mathematics_, In _Scientific Philosophy Today: Essays in Honor of Mario Bunge_, edited by Joseph Agassi and Robert S Cohen, 111–21. Boston: D. Reidel Publishing Co. (1981)

On [[categorical logic]] and [[topos theory]] (and establishing the [[relation between category theory and type theory|relation]] between [[simply-typed lambda calculus]] and [[cartesian closed categories]]):

* {#LambekScott86} [[Joachim Lambek]], [[Philip J. Scott]], *Introduction to higher order categorical logic*, Cambridge Studies in Advanced Mathematics **7** (1986) [[ISBN: 0-521-24665-2](https://www.cambridge.org/ae/academic/subjects/mathematics/logic-categories-and-sets/introduction-higher-order-categorical-logic?format=PB&isbn=9780521356534), [pdf](https://raw.githubusercontent.com/Mzk-Levi/texts/master/Lambek%20J.%2C%20Scott%20P.J.%20Introduction%20to%20Higher%20Order%20Categorical%20Logic.pdf)]

On [[computability]] and [[formal language]]:

* [[Joachim Lambek]] (with [[Michael Barr]]), *Programs, Grammars, Arguments*, lecture notes (2007) [[pdf](https://www.math.mcgill.ca/barr/papers/pga.pdf), [[LambekBarr-ProgramsGrammarArguments.pdf:file]]]

On [[injective hulls]] of [[partial order|partially ordered]] [[monoids]]:

* [[Joachim Lambek]], [[Michael Barr]], [[John Kennison]], [[Robert Raphael]], *Injective hulls of partially ordered monoids*, Theory Appl. Categories **26** 13 (2012) 338–348 [[tac:16-13](http://www.tac.mta.ca/tac/volumes/26/13/26-13abs.html)]

## Related entries

* [[lambda-calculus]]/[[relation between type theory and category theory]]

* [[biclosed monoidal category]]

* [[initial algebra]]

* [[linguistics]]

* [[categorial grammar]]

* [[Introduction to Higher-Order Categorical Logic]]

category: people

[[!redirects Joachim Lambek]]
[[!redirects Jim Lambek]]
[[!redirects Lambek]]


Joachim Wehler

* [personal page](https://www.mathematik.uni-muenchen.de/~wehler/)

## Selected writings

On [[Riemann surfaces]]:

* {#Wehler20} [[Joachim Wehler]], Section 15 in: *Riemann surfaces*, 2020 ([pdf](https://www.mathematik.uni-muenchen.de/~wehler/20190530_RiemannSurfacesScript.pdf))

category: people


Joan S. Birman

Joan Birman is an American mathematician who studies [[knots]] and [[braids]], and related subjects.

* [home page](http://www.math.columbia.edu/~jb/)

* [Wikipedia entry](http://en.wikipedia.org/wiki/Joan_Birman)

* [[Dan Margalit]], *The Mathematics of Joan Birman*, Notices of the AMS **66** 3 (2019) [[pdf](https://www.ams.org/journals/notices/201903/rnoti-p341.pdf), [pdf](https://www.ams.org/journals/notices/201903/201903FullIssue.pdf)]

## Selected writings

On [[braid groups]], [[links]] and [[mapping class groups]]:

* [[Joan S. Birman]], _Braids, links, and mapping class groups_, Princeton Univ Press (1975) [[ISBN:9780691081496](https://press.princeton.edu/books/paperback/9780691081496/braids-links-and-mapping-class-groups-am-82-volume-82), [preview pdf](https://api.pageplace.de/preview/DT0400.9781400881420_A26691398/preview-9781400881420_A26691398.pdf)]

On [[braid groups]], [[braid representations]] and some [[knot theory]]:

* [[Joan S. Birman]], [[Anatoly Libgober]] (eds.) *Braids*, Contemporary Mathematics **78** (1988) [[doi:10.1090/conm/078](http://dx.doi.org/10.1090/conm/078)]

category:people

[[!redirects Joan Birman]]


Joan Simón

* [institute page](https://higgs.ph.ed.ac.uk/people/simon-joan/)

## Selected writings

On the [[3-brane in 6d]]:

* [[Joaquim Gomis]], [[David Mateos]], [[Joan Simón]], [[Paul Townsend]], _Brane-Intersection Dynamics from Branes in Brane Backgrounds_, Phys. Lett. B430 (1998) 231-236 ([arXiv:hep-th/9803040](http://arxiv.org/abs/hep-th/9803040))

On [[M-waves]]:

* [[José Figueroa-O'Farrill]], [[Joan Simón]], section 2 of _Supersymmetric Kaluza-Klein reductions of M-waves and MKK-monopoles_, Class. Quant. Grav.19:6147-6174, 2002 ([arXiv:hep-th/0208108](https://arxiv.org/abs/hep-th/0208108))

On [[weight systems]] on [[chord diagrams]] as [[single trace observables]] in [[SYK-model]]-like [[AdS-CFT duality|dual]] descriptions of [[black hole thermodynamics]] (see at [[weight systems on chord diagrams in physics]]):

* {#BerkoozNarayanSimon18} [[Micha Berkooz]], [[Prithvi Narayan]], [[Joan Simón]], Section 2.1 of: _Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction_, JHEP 08 (2018) 192 ([arxiv:1806.04380](https://arxiv.org/abs/1806.04380))

category: people

[[!redirects Joan Simon]]


Joaquim Gomis

* webpage?

* [publications](http://en.scientificcommons.org/joaquim_gomis)

## Selected writings

On the [[3-brane in 6d]]:

* [[Joaquim Gomis]], [[David Mateos]], [[Joan Simón]], [[Paul Townsend]], _Brane-Intersection Dynamics from Branes in Brane Backgrounds_, Phys. Lett. B430 (1998) 231-236 ([arXiv:hep-th/9803040](http://arxiv.org/abs/hep-th/9803040))

category: people


Jocelyn Ireson-Paine

[[!redirects Jocelyn Ireson-Paine]]

+-- {: .rightHandSide}
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+--{: .hide}
[[!include contents]]
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I am a freelance programmer. My Website says more about this and other things I do.

But I was tempted into category theory, not least by my friends Hendrik Hilberdink, Răzvan Diaconescu, Petros Stefaneas, and José Bernardo Barros. And their supervisor, [[Joseph Goguen]].

Using experience gained from writing Web-based simulations of the economy, I have implemented some Web-based category theory demonstrations. Their main input page is here; and there is one more  that I've adapted to use the same notation as the nLab product page. If I could get funding, I'd like to make these easier for novices to learn from. Jamie Vicary offered to host them on the Oxford Computing Lab's servers: a good next step would be to tidy up and document the whole system, then make the source publicly available.

I'd also like to popularise category theory through my blog at Dr Dobbs. That's partly because I find it intrinsically fascinating; but also because I feel it has huge potential in Artificial Intelligence and cognitive science. I've written about that in an n-Category Café posting. Places where I think category theory could benefit AI and cognitive science include neural networks and their relation to logic and model theory, analogical reasoning, and holographic reduced representations.

One benefit is the tools category theory gives us to "achieve independence from the often overwhelmingly complex details of how things are represented or implemented". (I quote [[Joseph Goguen]]'s A categorical manifesto.) For example, holographic reduced representations represent symbolic structured data as high-dimensional vectors, storing and extracting items via operations similar to correlation and convolution. They can use the same operations to do analogical reasoning of the kind "What is to Sweden as Paris is to France?". This is important because any intelligent machine needs to do such reasoning; but it's something computers are notoriously bad at. If we could characterise HRRs categorically, it might help us discover which properties of their representational substrate are essential, and which merely accidental.

Perhaps — I don't know whether I'm joking or not — categorical characterisations could help us understand other phenomena. Could we find a universal property that a computational system satisfies if and only if it is conscious?!

Or — a simpler question, and one that must be sensible — that it satisfies if and only if it can represent and reason about itself? The latter would be an interesting project in dynamical systems; but perhaps it's assuming too much to regard the reasoner as a dynamical system.

Category theory also gives us tools for unifying disparate mathematical and computational phenomena. AI and cognitive science, of course, are full of disparate mathematical and computational phenomena, usually ones whose relatedness is badly understood. That is why my n-Category Café posting above mentioned neural networks: in it, I cited Michael Healy's paper  Category Theory Applied to Neural Modeling and Graphical Representations. He uses colimits, functors, and natural transformations to map concepts expressed as logic onto concepts represented in one kind of neural network.

As another example, I cited a paper by Goguen on analogical reasoning via "conceptual blending": Mathematical Models of
Cognitive Space and Time. He uses institutions and 3/2-colimits to (for example) represent the meaning of the word "houseboat" as an optimal blend of the meanings of "house" and "boat". Could we apply the same constructions to HRRs? That would unify two kinds of analogical reasoning implemented on very different representational substrates.

And as yet another, I suggest at [[generalisation as an adjunction]] that generalisation can be represented as an adjunction. More precisely, that generalisation and instantiation can be represented as an adjoint pair. Perhaps this could unify lots of different topics in machine learning.

Read the following quote from
Greg Egan's novel Incandescence. That's how I want category theory to unify cognitive science and AI:

'Interesting Truths' referred to a kind of theorem which captured subtle unifying insights between broad classes of mathematical structures. In between strict isomorphism — where the same structure recurred exactly in different guises — and the loosest of poetic analogies, Interesting Truths gathered together a panoply of apparently disparate systems by showing them all to be reflections of each other, albeit in a suitably warped mirror. Knowing, for example, that multiplying two positive integers was really the same as adding their logarithms revealed an exact correspondence between two algebraic systems that was useful, but not very deep. Seeing how a more sophisticated version of the same could be established for a vast array of more complex systems — from rotations in space to the symmetries of subatomic particles — unified great tracts of physics and mathematics, without collapsing them all into mere copies of a single example.

Incidentally, category theory also inspired me to invent a way of building spreadsheets from modules, and of storing these modules on the Web for anyone to download into their own spreadsheets.

+--{: .query}
Note the Markdown method for block-level code (which cannot produce a blank line at the beginning or end of the block), now also at the [[Sandbox]].  ---[[Toby Bartels]]
=--

category: people


Jocelyn Quaintance

* [institute page](https://online.seas.upenn.edu/team/jocelyn-quaintance/)

## Selected writings

On [[differential geometry]] and [[Lie groups]]:

* {#GallierQuaintance20a} [[Jean Gallier]], [[Jocelyn Quaintance]],  *Differential Geometry and Lie Groups -- A computational perspective*, Geometry and Computing **12**, Springer (2020) [[doi:10.1007/978-3-030-46040-2](https://doi.org/10.1007/978-3-030-46040-2), [webpage](https://www.cis.upenn.edu/~jean/gbooks/manif.html)]

* {#GallierQuaintance20b} [[Jean Gallier]], [[Jocelyn Quaintance]],  *Differential Geometry and Lie Groups -- A second course*, Geometry and Computing **13**, Springer (2020) [[doi:10.1007/978-3-030-46047-1](https://doi.org/10.1007/978-3-030-46047-1), [webpage](https://www.cis.upenn.edu/~jean/gbooks/manif.html)]

On [[ordinary homology]], [[ordinary cohomology]] and [[abelian sheaf cohomology]] in [[algebraic topology]], [[algebraic geometry]] and [[differential geometry]]:

* [[Jean Gallier]], [[Jocelyn Quaintance]], *Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry*, World Scientific (2022) [[doi:10.1142/12495](https://doi.org/10.1142/12495), [webpage](https://www.cis.upenn.edu/~jean/gbooks/sheaf-coho.html)]

category: people


Jocelyne Ishak

* [personal page](https://sites.google.com/view/jocelyneishak)

## Selected writings

On [[commutative ring]]-structure ([[E-infinity ring|$E_\infty$-ring]]-structure) in [[rational equivariant stable homotopy theory]] in general and in [[rational equivariant K-theory]] in particular:

* [[Anna Marie Bohmann]], [[Christy Hazel]], [[Jocelyne Ishak]], [[Magdalena Kędziorek]], [[Clover May]], *Naive-commutative structure on rational equivariant K-theory for abelian groups* ([arXiv:2002.01556](https://arxiv.org/abs/2002.01556))

* [[Anna Marie Bohmann]], [[Christy Hazel]], [[Jocelyne Ishak]], [[Magdalena Kędziorek]], [[Clover May]], *Genuine-commutative ring structure on rational equivariant K-theory for finite abelian groups* ([arXiv:2104.01079](https://arxiv.org/abs/2104.01079))

category: people


Jochen Heinloth

* [website](http://staff.science.uva.nl/~heinloth/)

## Selected writings

On [[differentiable stacks]]:

* [[Jochen Heinloth]], *Notes on differentiable stacks* (2004) [[pdf](https://math.nyu.edu/~tschinke/WS04/pdf/heinloth.pdf), [[Heinloth-DifferentiableStacks.pdf:file]]]

## Related entries

* [[stack]]

* [[geometric stack]]

category: people


Jock McOrist

Jock McOrist works on backgrounds in [[string theory]] and [[M-theory]], at Surrey University.

* [webpage](http://www.surrey.ac.uk/maths/people/jock_mcorist/index.htm)

## related $n$Lab pages

* [[heterotic string]], [[2d (2,0)-superconfromal sigma-model]]

category: people


Joe Corneli

* [webpage](http://metameso.org/~joe/)

## Related entries

* [[Planet Math]]

category: people


Joe Harris

* [Wikipedia entry](https://en.wikipedia.org/wiki/Joe_Harris_(mathematician)

## Selected writings

On [[representation theory]]:

* {#FultonHarris91} [[William Fulton]], [[Joe Harris]], _Representation Theory: a First Course_, Springer, Berlin, 1991 ([doi:10.1007/978-1-4612-0979-9](https://link.springer.com/book/10.1007/978-1-4612-0979-9))

## Related $n$Lab entries

* [[representation theory]], [[Young diagram]]

category: people

[[!redirects Joseph Harris]]


Joe Huxford

* [GoogleScholar page](https://scholar.google.com/citations?user=RCdk-qEAAAAJ&hl=en)

## Selected writings

On [[topological phases of matter]] via [[higher gauge theory|higher]] [[lattice gauge theory]]:

* [[Joe Huxford]], *The higher lattice gauge theory model for topological phases of matter*, PhD thesis, Oxford (2022) [[uuid:e789bf29-179b-4b79-9168-605bf8c035ba](https://ora.ox.ac.uk/objects/uuid:e789bf29-179b-4b79-9168-605bf8c035ba), [pdf](https://ora.ox.ac.uk/objects/uuid:e789bf29-179b-4b79-9168-605bf8c035ba/files/ddj52w5202)]

* [[Joe Huxford]], [[Steven H. Simon]], *Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview* [[arXiv:2202.08294](https://arxiv.org/abs/2202.08294)]

category: people


Joe Moeller

Joe Moeller is an NRC postdoc at NIST. He did his PhD at UCR under [[John Baez]].

* [website](https://joemathjoe.wordpress.com/)

## Selected writings

* [[John Baez]], [[Owen Lynch]], [[Joe Moeller]], _Compositional thermostatics_, [arXiv:2111.10315](https://arxiv.org/abs/2111.10315)

* [[John Baez]], [[Joe Moeller]], [[Todd Trimble]], _Schur functors and categorified plethysm_, [arXiv:2106.00190](https://arxiv.org/abs/2106.00190)

* [[Joe Moeller]], [[Christina Vasilakopoulou]], _Monoidal Grothendieck Construction_, Theory and Applications of Categories, Vol. 35, 2020, No. 31, pp 1159-1207. arXiv:[1809.00727](https://arxiv.org/abs/1809.00727)

* [[John Baez]], [[John Foley]], [[Joseph Moeller]], and [[Blake Pollard]], _Network Models_, Theory and Applications of Categories, Vol. 35, 2020, No. 20, pp 700-744. arXiv:[1711.00037](https://arxiv.org/abs/1711.00037)

* [[John Baez]], [[John Foley]], and [[Joe Moeller]] _Network Models from Petri Nets with Catalysts_, Compositionality, Volume 1, Issue 4, 2019. arXiv:[1904.03550](https://arxiv.org/abs/1904.03550), [DOI](https://doi.org/10.32408/compositionality-1-4)

* [[Joe Moeller]], _Noncommutative Network Models_, Mathematical Structures in Computer Science, 2019. arXiv:[1804.07402](https://arxiv.org/abs/1804.07402), [DOI](https://doi.org/10.1017/S0960129519000161)

On the [[monoidal Grothendieck construction]]:

* {#Moeller_Vasilakopoulou19} [[Joe Moeller]], [[Christina Vasilakopoulou]], _Monoidal Grothendieck Construction_, Theory and Applications of Categories, **35** 31 (2020) 1159-1207 [[arXiv:1809.00727](http://arxiv.org/abs/1809.00727), [tac:35-31](www.tac.mta.ca/tac/volumes/35/31/35-31abs.html)]

On [[FI-representations]] and [[representation stability]]:

* [[Joe Moeller]], *Extensions of representation stable categories* [[arXiv:2209.03879](https://arxiv.org/abs/2209.03879)]

category: people

[[!redirects Joseph Moeller]]


Joel David Hamkins

Joel David Hamkins is a set theorist.

* [English wikipedia entry](https://en.wikipedia.org/wiki/Joel_David_Hamkins)

* Personal blog: [mathematics and philosophy of the infinite](http://jdh.hamkins.org/)

## Related nLab pages

* [[set-theoretic multiverse]]

category: people


Joel E. Moore

* [personal page](https://physics.berkeley.edu/people/faculty/joel-moore)

## Selected writings

On [[topological insulators]]:

* [[Joel E. Moore]], [[Leon Balents]], *Topological invariants of time-reversal-invariant band structures*, Phys. Rev. B **75** (2007) 121306(R) $[$[doi:10.1103/PhysRevB.75.121306](https://doi.org/10.1103/PhysRevB.75.121306)$]$

* [[Joel E. Moore]], *The birth of topological insulators*, Nature volume 464, pages 194–198 (2010) ([doi:10.1038/nature08916](https://doi.org/10.1038/nature08916))

* [[M. Zahid Hasan]], [[Joel E. Moore]], *Three-Dimensional Topological Insulators*, Ann. Review.Condensed Matter Physics **2** (2011) 55-78 $[$[arXiv:1011.5462](https://arxiv.org/abs/1011.5462), [doi:10.1146/annurev-conmatphys-062910-140432](https://doi.org/10.1146/annurev-conmatphys-062910-140432)$]$

category: people

[[!redirects Joel Moore]]


Joel Kamnitzer

* [webpage](http://www.math.toronto.edu/jkamnitz/)

category: people


Joel Primack

* [webpage](http://scipp.ucsc.edu/personnel/profiles/primack.html)

* [Wikipedia entry](https://en.wikipedia.org/wiki/Joel_Primack)

## selected writings

* [[Joel Primack]], _Dark Matter and Structure Formation in the Universe_, Chapter 1 of _Formation of Structure in the Universe_, Proceedings of the Jerusalem Winter School 1996, edited by A. Dekel and J.P. Ostriker ([arXiv:astro-ph/9707285](https://arxiv.org/abs/astro-ph/9707285))

  (on [[structure formation]])

* {#PrimackCh6} [[Joel Primack]], _[The View from the Center of the Universe](http://viewfromthecenter.com/)_ Chapter 6: _What Size is the Universe? The Cosmic Uroboros_ ([pdf](http://physics.ucsc.edu/~joel/Chapter6.pdf), [[PrimackSizeOfUniverse.pdf:file]])

  (on the [[observable universe]])

## related $n$Lab entries

* [[structure formation]]

* [[observable universe]]

category: people


Joel Robbin

**Joel W. Robbin** is a mathematician at the University of Wisconsin at Madison. His thesis was in mathematical logics, under A. Church of Princeton; he also authored a textbook on logics and coauthored _Mathematical logic and computability_ with [Jerome Keisler](http://www.math.wisc.edu/~keisler).

From soon after his thesis, Robbin switches his main interests to [[dynamical system|dynamical systems]] of Morse--Smale type where he found several foundational results. He also worked in related questions of rigorous approaches to [[quantization]], [[symplectic geometry]] and [[symplectic topology]]; several of his articles are coauthored with [[Dietmar Salamon]].

At the time when MatLab was expensive for students, Robbin programmed an interpreter for a small subset MINI MatLab free for student's use and accompanying his undergraduate textbook on algebra; more recently he translated that subset to a java version.

* [homepage](http://www.math.wisc.edu/~robbin)

* J. W. Robbin, _Mathematical logic. A first course._ W. A. Benjamin, Inc., New York-Amsterdam 1969 xii+212 pp.
[MR0250846 (40 #4078)](http://www.ams.org/mathscinet-getitem?mr=0250846)

* R. Abraham, J. Robbin, _Transversal mappings and flows_, Benjamin, 1967

* Joel W. Robbin, _On structural stability._ Bull. Amer. Math. Soc. __76__  1970 723--726, [MR0261622 (41 #6235)](http://www.ams.org/mathscinet-getitem?mr=0261622)

* J. W. Robbin, D. Salamon, _[[Maslov index]] for paths_, Topology __32__  (1993), no. 4, 827--844, [doi](http://dx.doi.org/10.1016/0040-9383(93)90052-W), [pdf](http://www.math.ethz.ch/~salamon/PREPRINTS/maslov.pdf), [MR94i:58071](http://www.ams.org/mathscinet-getitem?mr=94i:58071)

* Joel W. Robbin, [[Dietmar Salamon]], _A construction of the Deligne--Mumford [[orbifold]]_, J. Eur. Math. Society, ISSN 1435-9855, Vol. 8, Nº 4, 2006, 611-699, [arXiv:math/0407090](http://arxiv.org/abs/math/0407090) [MR2009d:32012](http://www.ams.org/mathscinet-getitem?mr=2009d:32012), _Corrigendum_, J. Eur. Math. Soc. (JEMS)  __9__  (2007),  no. 4, 901--905, [doi](http://dx.doi.org/10.4171/JEMS/101)

* Joel W. Robbin, [[Dietmar A. Salamon]],  _Lyapunov maps, simplicial complexes and the Stone functor_, Ergodic Theory Dynam. Systems __12__ (1992), no. 1, 153--183, [doi](http://dx.doi.org/10.1017/S0143385700006647), [MR93h:58091](http://www.ams.org/mathscinet-getitem?mr=93h:58091)

* Joel W. Robbin, [[Yongbin Ruan]], [[Dietmar A. Salamon]],  _The moduli space of regular stable maps_,  Math. Z.  __259__  (2008),  no. 3, 525--574, [doi](http://dx.doi.org/10.1007/s00209-007-0237-x), [MR2010a:58014](http://www.ams.org/mathscinet-getitem?mr=2010a:58014)

* Vin de Silva, Joel Robbin, Dietmar Salamon, _Combinatorial Floer homology_, [arXiv/1205.0533](http://arxiv.org/abs/1205.0533)

* Joel W. Robbin, Dietmar A. Salamon, _Feynman path integrals and the metaplectic representation_, Math. Z. __221__ (1996), no. 2, 307–-335, [MR98f:58051](http://www.ams.org/mathscinet-getitem?mr=98f:58051), [doi](http://dx.doi.org/10.1007/BF02622118)

* Joel W. Robbin, Dietmar A. Salamon, _Phase functions and path integrals_, Symplectic geometry (Proc., ed. D. Salamon), 203–-226, London Math. Soc. Lecture Note Ser. __192__, Cambridge Univ. Press 1993, [[RobbinSalamonPhaseFunctionsPathIntegrals.djvu:file]].

category: people
[[!redirects Joel W. Robbin]]
[[!redirects J. W. Robbin]]


Joel S. Rozowsky

* [InSpire page](https://inspirehep.net/authors/991048)

## Selected writings

On the issue of excluding the $P^+ = 0$-mode in [[discretized light-cone quantization]]:

* [[Joel S. Rozowsky]], [[Charles B. Thorn]], *Spontaneous Symmetry Breaking at Infinite Momentum without $P^+$ Zero-Modes*, Phys. Rev. Lett. **85** (2000) 1614-1617 [[arXiv:hep-th/0003301](https://arxiv.org/abs/hep-th/0003301), [doi:10.1103/PhysRevLett.85.1614](https://doi.org/10.1103/PhysRevLett.85.1614)]

category: people

[[!redirects Joel Rozowsky]]


Joel Shapiro

* [webpage](http://www.physics.rutgers.edu/~shapiro/)

## Selected writings

On [[heterotic supergravity]] and the [[Green-Schwarz superstring]]:

* {#ShapiroTaylor87} [[Joel Shapiro]], Cyrus Taylor, _Superspace supergravity from the superstring_, Physics letter B **186** 1 (1987) [doi:10.1016/0370-2693(87)90514-4]

category: people


Jogesh Pati

* [Wikipedia entry](https://en.wikipedia.org/wiki/Jogesh_Pati)

## related $n$Lab entries

* [[quantum field theory]]

* [[GUT]]

category: people


Johan A. C. Kolk

* [personal page](https://www.uu.nl/staff/jackolk)

## Selected writings

On [[Lie groups]], [[Lie algebras]] and [[Lie integration]]:

* [[Hans Duistermaat]], [[Johan A. C. Kolk]], *Lie groups*, Springer (2000) [[doi:10.1007/978-3-642-56936-4](https://doi.org/10.1007/978-3-642-56936-4)]

[[!redirects J. A. C. Kolk]]
[[!redirects JAC Kolk]]


Johan Alm

Johan Alm was a PhD student in mathematical physics at [Stockholm University](http://www.su.se/) in the [geometry group](http://www2.math.su.se/matematik/geometri/research.html.en) with [Sergei Merkulov](http://www2.math.su.se/~sm/).

Alm did his masters thesis on _Infinitesimal extensions of Hirzebruch surfaces_ at University of Uppsala.

## Selected writings

* The Grothendieck-Teichmueller Lie algebra and Brown's dihedral moduli spaces. [arXiv:1805.06684](https://arxiv.org/abs/1805.06684)

* Universal algebraic structures on polyvector fields.  Doctoral Disseration, 2014.  Stockholm University.  [PDF](http://su.diva-portal.org/smash/record.jsf?pid=diva2%3A696219).

category: people


Johan Commelin

* [website](https://math.commelin.net/)

## Selected writings

* [[Kevin Buzzard]], [[Johan Commelin]], [[Patrick Massot]], *Formalising perfectoid spaces*, CPP 2020: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, Pages 299-312 ([doi:10.1145/3372885.3373830](https://doi.org/10.1145/3372885.3373830), [arXiv:1910.12320](https://arxiv.org/abs/1910.12320))

## Talks

* [[Johan Commelin]], *Liquid Tensor Experiment*, [[Homotopy Type Theory Electronic Seminar Talks]], 26 January 2023 ([slides](https://www.uwo.ca/math/faculty/kapulkin/seminars/hottestfiles/Commelin-2023-01-26-HoTTEST.pdf), [video](https://www.youtube.com/watch?v=gkeGLRrAkbY))

category:people


Johan Konter

* [webpage](http://www.math.northwestern.edu/~konter/)

category: people


Johan Louis Dupont

* [website](http://home.imf.au.dk/dupont/)

## Selected writings

On [[regulators]] and [[characteristic classes]] of [[flat connections]]:

* [[Johan Dupont]], [[Richard Hain]], Steven Zucker, _Regulators and characteristic classes of flat bundles_ ([arXiv:alg-geom/9202023](http://arxiv.org/abs/alg-geom/9202023))

On the [[homotopy groups]] of [[embedded cobordism categories]]:

* [[Marcel Bökstedt]], [[Johan Dupont]], [[Anne Marie Svane]], _Cobordism obstructions to independent vector fields_, Q. J. Math. 66 (2015), no. 1, 13-61 ([arXiv:1208.3542](https://arxiv.org/abs/1208.3542))

## Related $n$Lab entries #

* [[simplicial deRham complex]]

* [[Chern-Weil theory]]

* [[fiber integration in ordinary differential cohomology]]

category: people

[[!redirects Johan Dupont]]


Johan van Benthem

* [personal page](https://staff.fnwi.uva.nl/j.vanbenthem/)

* Wikipedia entry

## Selected writings

On [[modal logic]] ([[necessity]], [[possibility]], [[possible worlds semantics]], ...):

* {#BlackburnvanBenthemWolter07} [[Patrick Blackburn]], [[Johan van Benthem]], [[Frank Wolter]] (eds.), *The Handbook of Modal Logic*, Elsevier Amsterdam (2007) [[book webpage](https://cgi.csc.liv.ac.uk/~frank/MLHandbook/), [publisher page](https://www.sciencedirect.com/bookseries/studies-in-logic-and-practical-reasoning/vol/3/suppl/C)]

* [[Johan van Benthem]], *Modal Logic for Open Minds* (2010) [[ISBN:9781575865980](http://web.stanford.edu/group/cslipublications/cslipublications/site/9781575865980.shtml),[pdf](http://fenrong.net/teaching/mljvb.pdf), [webpage](https://archive.illc.uva.nl/lgc/MLoM/)]

category: people


Johann Fichte

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* [Wikipedia entry](http://en.wikipedia.org/wiki/Johann_Gottlieb_Fichte)
* [Stanford Encyclopedia of Philosophy entry](http://plato.stanford.edu/entries/johann-fichte/)

> Die Fichtesche Philosophie hat den großen Vorzug und das Wichtige, aufgestellt zu haben, daß Philosophie Wissenschaft aus höchstem Grundsatz sein muß, woraus alle Bestimmungen notwendig abgeleitet sind. Das Große ist die Einheit des Prinzips und der Versuch, wissenschaftlich konsequent den ganzen Inhalt des Bewußtseins daraus zu entwickeln oder, wie man es nannte, die ganze Welt zu konstruieren. Man hat sich darüber aufgehalten. Es ist Bedürfnis der Philosophie, eine lebendige Idee zu enthalten. Die Welt ist eine Blume, die aus einem Samenkorn ewig hervorgeht. ([Hegel, Lect Hist Phil](Lectures+on+the+History+of+Philosophy#FichteVorzugWissenschaft))

## related entries

* _[[Grundlage der gesamten Wissenschaftslehre]]_

* _[[Grundriss des Eigenthümlichen der Wissenschaftslehre]]_

## References

* [[Georg Hegel]], _[[Lectures on the History of Philosophy]] -- [Fichte](Lectures+on+the+History+of+Philosophy#Fichte)_

* [[David W. Wood]], _["Mathesis of the Mind": A Study of Fichte's Wissenschaftslehre and Geometry](http://www.amazon.com/Mathesis-Mind-Wissenschaftslehreand-Geometry-Fichte-Studien-Supplementa/dp/9042034912)_
  * NDPR review of [[David W. Wood]], _"Mathesis of the Mind": A Study of Fichte's Wissenschaftslehre and Geometry_: [http://ndpr.nd.edu/news/32285-mathesis-of-the-mind-a-study-of-fichte-s-wissenschaftslehre-and-geometry/](http://ndpr.nd.edu/news/32285-mathesis-of-the-mind-a-study-of-fichte-s-wissenschaftslehre-and-geometry/)
* [[David W. Wood]], "The 'Mathematical' Wissenschaftslehre: On a Late Fichtean Reflection of Novalis", in Dalia Nassar (ed) _[The Relevance of Romanticism: Essays on German Romantic Philosophy](http://books.google.com/books?id=V6rFAgAAQBAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)_ Oxford University Press (2014)

[[!redirects Fichte]]

[[!redirects Johann Gottlieb Fichte]]


Johann Leida

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=103016)

## Selected writings

On [[orbifolds]], [[orbifold cohomology]] and specifically on [[Chen-Ruan cohomology]] and [[orbifold K-theory]]:

* {#ALR07} [[Alejandro Adem]], [[Johann Leida]], [[Yongbin Ruan]], _Orbifolds and Stringy Topology_, Cambridge Tracts in Mathematics **171** (2007) ([doi:10.1017/CBO9780511543081](https://doi.org/10.1017/CBO9780511543081), [pdf](http://www.math.colostate.edu/~renzo/teaching/Orbifolds/Ruan.pdf))

category: people


Johann Rafelski

* [Wikipedia entry](https://en.wikipedia.org/wiki/Johann_Rafelski)

## Related $n$Lab entries

* [[interacting vacuum]]

* [[confinement]]

category: people


Johann Sigurdsson

* [Mathematics Genealogy page](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=86280)

## Selected writings

On [[parametrized stable homotopy theory]]:

* [[Peter May]], [[Johann Sigurdsson]], _[[Parametrized Homotopy Theory]]_, Mathematical Surveys and Monographs, vol. 132, AMS 2006  ([ISBN:978-0-8218-3922-5](https://bookstore.ams.org/surv-132), [arXiv:math/0411656](https://arxiv.org/abs/math/0411656), [pdf]( http://www.math.uchicago.edu/~may/EXTHEORY/MaySig.pdf))

category: people


Johann Sonner

* [MathGeneralogy page](https://mathgenealogy.org/id.php?id=14697)

## Selected writings

On [[mathematical foundations]] for [[category theory]] via [[Grothendieck universes]]:

* [[Johann Sonner]], *On the formal definition of categories*, Math. Zeitschr. **80** (1962) 163-176 [[eudml:170093](https://eudml.org/doc/170093), [[Sonner-FormalDefCategories.pdf:file]]]

category: people


Johanna Erdmenger

* [personal page](https://wwwth.mpp.mpg.de/members/jke/)

* [GoogleScholar page](https://scholar.google.com/citations?user=XhPrAVsAAAAJ&hl=en)

## Selected writings

On [[mesons]] in [[holographic QCD]]:

* [[Johanna Erdmenger]], [[Nick Evans]], [[Ingo Kirsch]], [[Ed Threlfall]], *Mesons in Gauge/Gravity Duals - A Review*, Eur. Phys. J. A **35** (2008) 81-133 [[arXiv:0711.4467](https://arxiv.org/abs/0711.4467), [doi:10.1140/epja/i2007-10540-1](https://doi.org/10.1140/epja/i2007-10540-1)]

On the [[Higgs field]] in [[holographic QCD]]:

* [[Johanna Erdmenger]], [[Nick Evans]], [[Werner Porod]], [[Konstantinos Rigatos]], *Gauge/gravity dual dynamics for the strongly coupled sector of composite Higgs models*, JHEP **58** (2021) [[arXiv:2010.10279](https://arxiv.org/abs/2010.10279), doi:10.1007/JHEP02(2021)058]

category: people


Johannes Ebert

* [website](http://www.math.uni-bonn.de/~ebert/)

## Selected writings

On [[geometric realization of topological stacks|geometric realization]] of [[topological stacks]]:

* [[Johannes Ebert]], *The homotopy type of a topological stack* ([arXiv:0901.3295](https://arxiv.org/abs/0901.3295))

On [[semi-simplicial topological spaces]]:

* [[Johannes Ebert]], [[Oscar Randal-Williams]], *Semi-simplicial spaces*, Algebr. Geom. Topol. 19 (2019) 2099-2150 ([arXiv:1705.03774](https://arxiv.org/abs/1705.03774))

category: people


Johannes Huebschmann

* [website](http://math.univ-lille1.fr/~huebschm/)

## Selected writings

On the history of [[Lie algebras]], [[differential crossed modules]] and [[Lie-Rinehart algebras]]:

* {#Huebschmann22} [[Johannes Huebschmann]], *On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras* [[arXiv:2208.02539](https://arxiv.org/abs/2208.02539)]

On the history of this and related concepts:

* {#Huebschmann22} [[Johannes Huebschmann]], *On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras* [[arXiv:2208.02539](https://arxiv.org/abs/2208.02539)]

## Related entries

* [[Lie-Rinehart pair]]

* [[identity among the relations]]

category: people
[[!redirects J. Huebschmann]]


Johannes Huisman

* [webpage](http://pageperso.univ-brest.fr/~huisman/)

## related entries

* [[real analytic space]]

[[!redirects Johan Huisman]]

category: people


Johannes Kepler

* Wikipedia, _[Johannes Kepler](https://en.wikipedia.org/wiki/Johannes_Kepler)_

## related $n$Lab entries

* [[Platonic solid]], [[The Music of the Spheres]]

category: people

[[!redirects Kepler]]


Johannes Schmude

* [webpage](http://ribf.riken.jp/~jschmude/index.html)

## Selected writings

On [[D6-branes]] lifting to [[Kaluza-Klein monopoles]] in [[M-theory]]:

* {#GaillardSchmude09} [[Jérôme Gaillard]], [[Johannes Schmude]], _The lift of type IIA supergravity with D6 sources: M-theory with torsion_, JHEP 1002:032,2010 ([arXiv:0908.0305](http://arxiv.org/abs/0908.0305))

## Related $n$Lab entries

* [[Kaluza-Klein monopole]]

category: people


Johannes Walcher

* [personal page](https://web.mathi.uni-heidelberg.de/physmath/walcher)

* [institute page](https://www.mathi.uni-heidelberg.de/~walcher/)

* [inspire page](https://inspirehep.net/authors/984280)

## Selected writings

On [[moduli stabilization]] in [[non-geometric string vacua]]:

* [[Katrin Becker]], [[Melanie Becker]], [[Cumrun Vafa]], [[Johannes Walcher]], _Moduli Stabilization in Non-Geometric Backgrounds_,  Nucl. Phys. B **770** (2007) 1-46 [[arXiv:hep-th/0611001](https://arxiv.org/abs/hep-th/0611001)]

On [[RR-field tadpole cancellation]] for the [[topological string]]:

* {#Walcher07} [[Johannes Walcher]], _Evidence for Tadpole Cancellation in the Topological String_, Communications in Number Theory and Physics **3** 1 (2009) [[arXiv:0712.2775](https://arxiv.org/abs/0712.2775)]

On the [[CP^1 sigma-model|$\mathbb{C}P^1$ sigma-model]]:

* [[Shmuel Elitzur]], [[Yaron Oz]], [[Eliezer Rabinovici]], [[Johannes Walcher]], *Open/Closed Topological $\mathbb{C}P^1$ Sigma Model Revisited*,  J. High Energ. Phys. **2012** 101 (2012) [[arXiv:1106.2967](https://arxiv.org/abs/1106.2967)]

category: people


John A. Smolin

* [Wikipedia entry](https://en.wikipedia.org/wiki/John_A._Smolin)

* [GoogleScholar page](https://scholar.google.com/citations?user=wGK-MJYAAAAJ&hl=en)

## Selected writings

Influential early discussion of ([[controlled quantum gate|controlled]]) [[quantum logic gates]]:

* {#BBCDMSSSW95} [[Adriano Barenco]], [[Charles H. Bennett]], [[Richard Cleve]], [[David P. DiVincenzo]], [[Norman Margolus]], [[Peter W. Shor]], [[Tycho Sleator]], [[John A. Smolin]], [[Harald Weinfurter]], *Elementary gates for quantum computation*, Phys. Rev. A**52** (1995) 3457 [[arXiv:quant-ph/9503016](https://arxiv.org/abs/quant-ph/9503016), [doi:10.1103/PhysRevA.52.3457](https://doi.org/10.1103/PhysRevA.52.3457)]

category: people


John Alexander Cruz Morales

* [maths genealogy page](http://www.genealogy.math.ndsu.nodak.edu/id.php?id=178856)

## related $n$Lab pages

* [[model theory and physics]]

category: people


John Arthur Todd

* [Wikipedia entry](http://en.wikipedia.org/wiki/J._A._Todd)

## related entries

* [[Todd class]]

category: people

[[!redirects John Todd]]


John Baez

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I work on mathematical physics --- which I interpret broadly as 'math that could be of interest in physics, and physics that could be of interest in math'.  I'm especially interested in $n$-categories and their applications.  I've spent a lot of time explaining these subjects on the web.   You can see a sampling below.  For a lot more stuff, see my [website](http://math.ucr.edu/home/baez/).

If you visit my [[John Baez:HomePage|personal web]] here, you'll see my work with James Dolan on doctrines in algebraic geometry, and the preface of a book I edited with Peter May, called _[[Towards Higher Categories]]_.

#Web Pages

[Symmetries, Groups, and Categories](http://math.ucr.edu/home/baez/symmetries.html)

[Categories, Quantization and Much More](http://math.ucr.edu/home/baez/categories.html)

[Tangles](http://math.ucr.edu/home/baez/tangles.html)

[Topos Theory in a Nutshell](http://math.ucr.edu/home/baez/topos.html)

[The Tale of $n$-Categories](http://math.ucr.edu/home/baez/week73.html#tale)

[The Tale of Groupoidification](http://math.ucr.edu/home/baez/groupoidification/)

#Papers

[Higher-dimensional algebra and topological quantum field theory](http://arxiv.org/abs/q-alg/9503002), with
James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105.

[Higher-dimensional algebra I: braided monoidal 2-categories](http://math.ucr.edu/home/baez/bm2cat.ps), with Martin
Neuchl, Adv. Math. 121 (1996), 196-244.

[An introduction to $n$-categories](http://arxiv.org/abs/q-alg/9705009), in
7th Conference on Category Theory and Computer Science, eds.
E. Moggi and G. Rosolini, Springer Lecture Notes in
Computer Science vol. 1290, Springer, Berlin, 1997.

[Higher-dimensional algebra II: 2-Hilbert spaces](http://arxiv.org/abs/q-alg/9609018),
Adv. Math. 127 (1997), 125-189.

[Higher-dimensional algebra III: $n$-categories
and the algebra of opetopes](http://arxiv.org/abs/q-alg/9702014), with James Dolan, Adv. Math. 135 (1998), 145-206.

[Spin foam models](http://arxiv.org/abs/gr-qc/9709052), Class. Quantum Grav. 15 (1998), 1827-1858.

[Categorification](http://arxiv.org/abs/math.QA/9802029), with James Dolan, in Higher Category
Theory, eds. Ezra Getzler and Mikhail Kapranov,
Contemp. Math. 230, American
Mathematical Society, Providence, Rhode Island, 1998, pp. 1-36.

[An introduction to spin foam models of
BF theory and quantum gravity](http://arxiv.org/abs/gr-qc/9905087), in Geometry and Quantum Physics, eds. Helmut
Gausterer and Harald Grosse, Springer, Berlin, 2000,
pp. 25-93.

[From finite sets to Feynman diagrams](http://arxiv.org/abs/math.QA/0004133), with James Dolan, in Mathematics Unlimited - 2001
and Beyond, vol. 1, eds. Björn Engquist and Wilfried Schmid, Springer,
Berlin, 2001, pp. 29-50.

[Higher-dimensional algebra and Planck-scale physics](http://arxiv.org/abs/gr-qc/9902017),
in Physics Meets Philosophy at the Planck Length, eds.
Craig Callender and Nick Huggett, Cambridge U. Press, Cambridge, 2001,
pp. 177-195.  Also available as a [webpage](http://math.ucr.edu/home/baez/planck/).

[Higher-dimensional algebra IV: 2-tangles](http://arxiv.org/abs/math.QA/9811139), with Laurel Langford,
Adv. Math. 180 (2003), 705-764.

[Higher-dimensional
algebra V: 2-groups](http://arxiv.org/abs/math.QA/0307200), with Aaron D. Lauda, [Theory
and Applications of Categories](http://www.tac.mta.ca/tac/volumes/12/14/12-14abs.html) 12 (2004), 423-491.

[Higher-dimensional
algebra VI: Lie 2-algebras](http://arxiv.org/abs/math.QA/0307263), with Alissa S. Crans, [Theory
and Applications of Categories](http://www.tac.mta.ca/tac/volumes/12/15/12-15abs.html) 12 (2004), 492-528.

[Quantum quandaries:
a category-theoretic perspective](http://arxiv.org/abs/quant-ph/0404040), in
Structural Foundations of Quantum Gravity,
eds. Steven French, Dean Rickles and Juha Saatsi, Oxford U. Press,Oxford, 2006, pp. 240-265. Also available as a [webpage](http://math.ucr.edu/home/baez/quantum/)

[Higher gauge theory](http://arxiv.org/abs/math.DG/0511710),
with Urs Schreiber, in
Categories in Algebra, Geometry and Mathematical
Physics, eds. Alexei Davydov, Michael Batanin,
Michael Johnson, Stephen Lack and Amnon Neeman, Contemp. Math. 431, American Mathematical Society, Providence, Rhode Island, 2007, pp. 7-30.

[From loop groups
to 2-groups](http://arxiv.org/abs/math.QA/0504123)
with Alissa S. Crans, Danny Stevenson and Urs Schreiber,
[Homotopy,
Homology and Applications](http://intlpress.com/HHA/v9/n2/a4/), 9 (2007), 101-135.

[Lectures on
$n$-categories and cohomology](http://arxiv.org/abs/math.CT/0608420), with Michael Shulman, to appear
in n-Categories: Foundations and Applications, eds.
John Baez and Peter May.

[The classifying space of a
topological 2-group](http://arxiv.org/abs/0801.3843), with Danny Stevenson, to appear in the
proceedings of the 2007 Abel Symposium, eds. Nils Baas et al.

[Convenient categories of smooth spaces](http://arXiv.org/abs/0807.1704), with Alex Hoffnung.

[Categorified symplectic geometry and the classical string](http://arXiv.org/abs/0808.0246), with Alex Hoffnung and Chris Rogers.

[Categorified symplectic geometry and the string Lie 2-algebra](http://arxiv.org/abs/0901.4721), with Christopher L. Rogers.

[Representations of 2-groups on higher Hilbert
spaces](http://arxiv.org/abs/0812.4969), with Aristide Baratin, Laurent Freidel and Derek Wise.

[Physics, topology, logic and computation:
a Rosetta Stone](http://arxiv.org/abs/0903.0340), with [[Mike Stay]], in New structures for physics, pp. 95-172. Springer, Berlin, Heidelberg, 2010.

[Groupoidification made easy](http://arxiv.org/abs/0812.4864), with Alexander E. Hoffnung and Christopher D. Walker.

[A history of n-categorical physics](http://math.ucr.edu/home/baez/history.pdf),
with Aaron Lauda, in proceedings of
Deep Beauty: Mathematical Innovation and the Search for
an Underlying Intelligibility of the Quantum World, ed.
Hans Halvorson.
category: people

[[!redirects John C. Baez]]
[[!redirects John C Baez]]


John Barrett

* [Wikipedia entry](http://en.wikipedia.org/wiki/John_W._Barrett)

## Selected writings
 {#SelectedWritings}

On [[Regge calculus]]:

* {#Barrett87} [[John Barrett]], _The geometry of classical Regge calculus_, Classical and Quantum Gravity, Volume 4, Number 6, 1987 ([doi:10.1088/0264-9381/4/6/015/meta](http://iopscience.iop.org/article/10.1088/0264-9381/4/6/015/meta))

On [[parallel transport]]:

* [[John Barrett]], _Holonomy and path structures in general relativity and Yang-Mills theory_, Int. J. of Theor. Phys., Iiol. 30, No. 9, 1991 ([doi:10.1007/BF00671007](https://doi.org/10.1007/BF00671007))

On [[spherical category|spherical]] [[fusion categories]] and the [[Turaev-Viro model]]:

* [[John Barrett]], [[Bruce Westbury]], _Invariants of piecewise-linear 3-manifolds_, Trans. Amer. Math. Soc. 348 (1996), no. 10, 3997–4022, ([doi:10.1090/S0002-9947-96-01660-1](https://doi.org/10.1090/S0002-9947-96-01660-1), MR1357878)

* [[John Barrett]], [[Bruce Westbury]], _Spherical Categories_, Adv. Math. 143:357-375, 1999 ([arXiv:hep-th/9310164](http://arxiv.org/abs/hep-th/9310164), [doi:10.1006/aima.1998.1800](https://doi.org/10.1006/aima.1998.1800))

On the relation between the [[Turaev-Viro model]] and the [[Crane-Yetter model]]:

* {#BarrettGarciaIslasMartins04} [[John Barrett]], J. Garcia-Islas, [[João Faria Martins]], _Observables in the Turaev-Viro and Crane-Yetter models_, J. Math. Phys. 48:093508, 2007 ([arXiv:math/0411281](http://arxiv.org/abs/math/0411281))

On the [[Connes-Lott model]]:

* {#Barrett07} [[John Barrett]], _A Lorentzian version of the non-commutative geometry of the standard model of particle physics_, J. Math. Phys. 48:012303, 2007 ([arXiv:hep-th/0608221](http://arxiv.org/abs/hep-th/0608221), [doi:10.1063/1.2408400](https://doi.org/10.1063/1.2408400))

category: people


John Bell

John Stewart Bell was an Irish physicist credited with developing one of the most profound theorems in [[quantum physics]], now known as [[Bell's theorem]].

* [biography](http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Bell_John.html) (detailed)

* [biography](http://en.wikipedia.org/wiki/John_Stewart_Bell) (detailed)

> (beware that there is also the mathematician and philosopher [[John Lane Bell]])

See also:

* Marian Kupczynski, *My discussions of quantum foundations with John Stewart Bell* [[arXiv:2210.16837](https://arxiv.org/abs/2210.16837)]

## Related

* [[chiral anomaly]]

* [[Bell's theorem]]

* [[Kochen-Specker theorem]]

* [[Gleason's theorem]]

* [[beable]]

* [[interpretation of quantum mechanics]]

category: people

[[!redirects John Stewart Bell]]


John Bourke

* [personal page](http://www.math.muni.cz/~bourkej/)

* [MathematicsGenealogy page](https://www.mathgenealogy.org/id.php?id=150865)

## Selected writings

* [list of arXiv preprints](http://arxiv.org/find/math/1/au:+Bourke_J/0/1/0/all/0/1)

On [[algebraic weak factorization systems]]:

* [[John Bourke]], _An orthogonal approach to algebraic weak factorisation systems_, Journal of Pure and Applied Algebra **227** 6 (2023) 107294 [[arxiv:2204.09584](https://arxiv.org/abs/2204.09584), [doi:10.1016/j.jpaa.2022.107294](https://doi.org/10.1016/j.jpaa.2022.107294)]

[[skew monoidal|Skew monoidal]] closed structures on the category of [[Gray categories]] are considered in:

* [[John Bourke]], [[Gabriele Lobbia]], _A skew approach to enrichment for Gray-categories_, (2022). [[arXiv:2212.12358](https://arxiv.org/abs/2212.12358)]

category: people


John Brodie

* [Wikipedia entry](https://en.wikipedia.org/wiki/John_H._Brodie)

## Selected writings

On [[D-branes]] [[brane intersection|intersecting]] [[NS5-branes]]:

* {#BrodieHanany97} [[John Brodie]], [[Amihay Hanany]], _Type IIA Superstrings, Chiral Symmetry, and N=1 4D Gauge Theory Dualities_, Nucl.Phys. B506 (1997) 157-182 ([arXiv:hep-th/9704043](https://arxiv.org/abs/hep-th/9704043))

On [[Chern-Simons theories]] arising from the [[higher WZ term]] on [[intersecting brane|intersecting]] [[super p-branes]]:

* {#Brodie00} [[John Brodie]], _D-branes in Massive IIA and Solitons in Chern-Simons Theory_, JHEP 0111:014, 2001 ([arXiv:hep-th/0012068](https://arxiv.org/abs/hep-th/0012068))

## Related $n$Lab entries

* [[NS5-brane]]

category: people


John C. Reynolds

**John C. Reynolds** (1935-2013) was an American computer scientist who made fundamental contributions to the theory of programming languages.

## Links

* [Wikipedia entry](https://en.wikipedia.org/wiki/John_C._Reynolds)
* Stephen Brookes, Peter W. O'Hearn and Uday Reddy, _[The Essence of Reynolds](http://www.cs.bham.ac.uk/~udr/papers/EssenceOfReynolds.pdf)_, POPL 2014.
* [webpage](http://www.cs.cmu.edu/~jcr/)

## Related entries

* [[polymorphism]]
* [[logical relation]]
* [[coercion]]
* [[continuation-passing style]]
* [[programming language]]

[[!redirects John Reynolds]]


John C. Slater

* [John C. Slater](https://en.wikipedia.org/wiki/John_C._Slater)

## Selected writings

On the [[quantum physics]] of [[electron]] [[energy]]-levels of [[atoms]] and [[molecules]] taking into account electron [[interaction]], and for that purpose (re-)introducing the method now known as *[[Slater determinants]]*:

* [[John C. Slater]], *The Theory of Complex Spectra*, Phys. Rev. **34** (1929) 1293 $[$[doi:10.1103/PhysRev.34.1293](https://doi.org/10.1103/PhysRev.34.1293)$]$

On [[solid state physics]]:

* {#JS75} [[John Slater]], *Solid-State and Molecular Theory: A Scientific Biography*, Wiley (1975) [[archive](https://archive.org/details/solidstatemolecu00slat/)]

## Related entries

* [[Slater determinant]]

* [[Gruppenpest]]

[[!redirects John Slater]]


John Cardy

* [webpage](http://www-thphys.physics.ox.ac.uk/people/JohnCardy/)

## Selected writings

On [[logarithmic CFT]]:

* [[John Cardy]], *Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications*, J. Phys. A: Math. Theor. **46** (2013) 494001  $[$[arXiv:1302.4279](http://arxiv.org/abs/1302.4279), [doi:10.1088/1751-8113/46/49/494001](https://doi.org/10.1088/1751-8113/46/49/494001)$]$

On the [[TT deformation]] of [[2d CFT]]:

* [[John Cardy]], _The $T \bar T$ deformation of quantum field theory_, 2018 ([pdf](https://icmp2018.org/sites/icmp/files/slides/0900_cardy_symposia_thursday.pdf), [[CardyTTDeformation.pdf:file]])

* [[John Cardy]], Benjamin Doyon, _$T \bar T$deformations and the width of fundamental particles_ ([arXiv:2010.15733](https://arxiv.org/abs/2010.15733))

## Related entries

* [[conformal field theory]]

category: people


John Cartmell

* [github](https://github.com/JohnWCartmell)

* [Entity Modelling website](http://www.entitymodelling.org/home/overview.html)

## Selected writings

On [[generalized algebraic theories]] and [[contextual categories]] and the [[categorical model of dependent types]]:

* {#Cartmell1978} [[John Cartmell]], *Generalised Algebraic Theories and Contextual Categories*, PhD thesis, Oxford University (1978) [[[Cartmell-Thesis.pdf:file]]]

* {#Cartmell86} [[John Cartmell]], *Generalised Algebraic Theories and Contextual Categories*, Annals of Pure and Applied Logic, **32** (1986) 209-243  [[doi:10.1016/0168-0072(86)90053-9](http://dx.doi.org/10.1016/0168-0072%2886%2990053-9)]

category: people


John D. Berman

* [personal page](https://web.ma.utexas.edu/users/jberman/)

## Selected writings

On [[categorical algebra]] and ([[equivariant stable homotopy theory|stable]]) [[equivariant homotopy theory]]:

* {#Berman18} [[John D. Berman]], p. 92 of: _Categorified algebra and equivariant homotopy theory_, PhD thesis 2018  ([arXiv:1805.08745](https://arxiv.org/abs/1805.08745))

On [[enriched (∞,1)-categories]]:

* [[John D. Berman]], *Enriched infinity categories I: enriched presheaves* ([arXiv:2008.11323](https://arxiv.org/abs/2008.11323))

On [[algebraic (∞,1)-theories]]:

* [[John D. Berman]], _Higher Lawvere theories_ ([arXiv:1903.02991](https://arxiv.org/abs/1903.02991))

On the idea of a [[symmetric monoidal category]] as a module over a commutative [[semiring category]]:

* [[John D. Berman]], _On the commutative algebra of categories_, Algebraic and Geometric Topology, 18(5):2963–3012, August 2018, ([arXiv:1606.05606](https://arxiv.org/abs/1606.05606)).

category: people

[[!redirects John Berman]]


John D. Jackson

* Wikipedia entry

## Selected writings

On [[classical field theory|classical]] [[electrodynamics]]:

* [[John D. Jackson]], *Classical Electrodynamics*, Wiley (1962, 1975, 1998) [[ISBN:978-0-471-30932-1](https://www.wiley.com/en-us/Classical+Electrodynamics%2C+3rd+Edition-p-9780471309321), Wikipedia entry]

category: people

[[!redirects John David Jackson]]
[[!redirects John Jackson ]]