2009 May changes

+-- {: .rightHandSide}
+-- {: .toc .clickDown tabindex="0"}
### Archive
+-- {: .hide}
[[!include all changes]]
=--
=--
=--

Archive of changes made during May 2009.
The substantive content of this page should **not** be altered.
For past versions of this page beyond its own history, start [here](http://ncatlab.org/nlab/revision/2009+June+changes/773) and work backwards.

***

# 2009-05-30 #

*  [[Toby Bartels]]:  I don\'t understand $diag$ at [[Atiyah Lie groupoid]].

* [[Urs Schreiber|Urs]]:

  * started [[connection on a bundle]] in reply to discussion [here](http://sbseminar.wordpress.com/2009/05/28/local-systems-what-do-you-know-about-connections/#comment-5791)

  * added to [[distributor]] the description in terms of colimit preserving functors on presheaf categories and added corresponding remarks at the beginning of [[symmetric monoidal (infinity,1)-category of presentable (infinity,1)-categories]]

  * created [[Atiyah Lie-groupoid]] and [[principal bundle]] to link to from the blog discussion [here](http://sbseminar.wordpress.com/2009/05/28/local-systems-what-do-you-know-about-connections/#comment-5791)

*  [[Toby Bartels]]:
   *  A new query at [[sieve]].
   *  Wrote [[finitely cocomplete category]] by copying [[finitely complete category]] and cutting it down.
   *  Responded to Bruce at [[coverage]], to Urs at [[sieve]], and to Eric at [[category of elements]].

# 2009-05-29 #

*  [[Todd Trimble]] kindly created [[quasitopos]].

* [[Urs Schreiber|Urs]]

  * reacted to [[Bruce Bartlett|Bruce]] at [[sieve]]

* [[Bruce Bartlett|Bruce]]

  * added a question at [[coverage]]

  * added comments to [[sieve]]

* [[Urs Schreiber|Urs]]

  * added a long section "A detailed description of what's going on" to [[sieve]], meant to be pedagogical, veery small-stepped. I'd be interested to hear from non--experts to which extent they find this bit helpful

  * replied (to [[Toby Bartels|Toby]], I presume?) at [[sieve]]

  * created [[Dijkgraaf-Witten theory]]

# 2009-05-28 #

* [[Urs Schreiber|Urs]]

  * created [[On the Classification of Topological Field Theories]], [[factorization algebra]]

  * created [[category of generalized elements]] as a place for the material that was at [[Exploding a Category]] -- I am voting for not using that explosive terminology

  * expanded [[path category]] and created [[Moore path category]] in the process

* [[David Roberts]]: Added comment to [[plus construction]] re disambiguation (recall the [[Quillen plus construction]]).

# 2009-05-27 #

*  [[Toby Bartels]]:  Last night, I made some lists of entries relevant to [[constructive mathematics]], starting with the back links and classifying them.  (Hopefully the third list will become so large that we can\'t really use it, but for now I want to keep track of which entries have that material.)

* [[Urs Schreiber|Urs]]

  * created [[Quantization as a Kan Extension]]

  * created [[plus construction]] -- the material that should go there is currently at [[sheaf]]; should be extracted from there eventually

  * added a link to the great Catsters video material to [[limits and colimits by example]] and created [[The Catsters]] and [[Eugenia Cheng]]

* [[David Corfield|David]] created [[extended natural numbers]], [[corecursion]], and [[coalgebra for an endofunctor]]. Moved proof of terminal coalgebra being fixed point to [[terminal coalgebra]]. 'Coalgebra' still needs disambiguation.

# 2009-05-26 #

* [[Bruce Bartlett|Bruce]] filled in a small thing at [[semisimple category]].

* [[Urs Schreiber|Urs]]:

  * created [[path integral]]

  * added to [[sieve]] a -- potentially long-winded -- lemma with detailed proof  that spells out details of the fact that every subfunctor is the coimage of a morphism out of a coproduct of representables

  * created [[separated presheaf]]

  * further worked on the section "in terms of geometric embedding" at [[sheaf]]

# 2009-05-25 #

*  [[Toby Bartels]]:  Copied comments on Google and page names to the Café [here](http://golem.ph.utexas.edu/category/2009/05/nlab_more_general_discussion.html#c024021).

* [[Urs Schreiber|Urs]]

  * expanded and restructured [[sieve]] -- introduced the explicit _distinction_ between the notion of _sieve_ and that of _subfunctor_ and made their _bijection_ explicit: this seems to be the standard way that "sieve" is used in the literature: authors don't seem to say "sieve" synonymously with "subfunctor", but say "sieve" if they explicitly mean the _set_ of elements of the subfunctor. There is a bijection, but not an equality of concepts.

  * further expanded [[image]] and [[coimage]]

  * edited and replied at [[semisimple category]]

* [[Bruce Bartlett|Bruce]] responded to comments at [[semisimple category]]...and then got stuck. Can anyone help?  Update from Future Bruce to Past Bruce: solved.

* [[Zoran Skoda]]: *as far as google (and other search machine's) counterarguments of Toby (see down 22. may) I still disagree. I do care if our stuff is well indexed and hence better used by anybody looking for answer at the google including us; and I do not care about vanity issues of pro or contra google movements. If somebody gets directed to a less relevant page this is creating noise, and showing a less convenient side of our work. If effectivity is not important why are we doing this ?

* [[Urs Schreiber|Urs]]

  * further developed the section "In terms of geometric embedding" at [[sheaf]], but will continue later. I am lacking (at least) one argument in one of the proofs currently...

  * created [[Bertrand Toën]] (and [[Bertrand Toen]] as a redirect)

# 2009-05-24 #

*  [[Toby Bartels]]:
   *  Cleaned up [[Cauchy space]] a bit.
   *  An answer for [[Mike Shulman]] at [[subsequential space]].
   *  A question for [[Bruce Bartlett]] at [[semisimple category]].

* [[Todd Trimble|Todd]]: Added a section "morphisms of manifolds" to [[manifold]] which attempts to enlarge the notion of pseudogroup, so as to get general notions of map for general notions of manifold. However, this is "original research" and should be vetted -- I don't see the enlarged notion (or an equivalent) in any of the literature I've read.

* [[Bruce Bartlett|Bruce]]: started/added material to some pages related to fusion categories, like [[fusion category]], [[Pivotal symbols]] (this name needs to be changed to fit the naming conventions), [[semisimple category]] and [[rigid monoidal category]].

* [[Urs Schreiber|Urs]]:

  * started expanding [[sheaf]] -- my goal is (as now indicated) to give a full derivation of how a geometric morphism into a presheaf category defines a Grothendieck topology and sheaves with respect to that -- but my machine's battery runs low and will leave me offline any minute now, so will have to continue later (darn technology...)

  * many thanks to [[Bruce Bartlett|Bruce]] for expanding [[fusion category]] and creating the relevant further entries

  * created a stub for [[fusion category]]

  * created a stub for [[String field theory]]

  * created [[A Survey of Cohomological Physics]]

  * added cross-links to [[monoidal category]] and [[manifold]]

# 2009-05-23 #

*  [[Toby Bartels]]:
   *  Created [[Banach space]]s.  I need to at least describe products and coproducts in $Ban$.
   *  Another example, Banach spaces, at [[internal hom]].
   *  Looking at other things that Urs has done, the problem may be this:  If you want to put an equation within a bullet list, then you either have to put no blank lines between the equation and the surrounding text
$$
like this
$$
or put enough spacing before the equation to match the indentation of the list

      $$
      like this
      $$

      or, of course, both
      $$
      like this
      $$
      but it will fall outside of the bullet list if you do neither

$$
like this
$$

* [[Bruce Bartlett|Bruce]]:
   * Added example of the internal hom in super vector spaces to [[internal hom]].
   * Urs: I tried to understand what went wrong with your query box example for [[Tychonoff theorem]] but I think the roll-back has removed the original problem from the records.

# 2009-05-22 #

*  [[Toby Bartels]]:
   *  Expanded [[centipede mathematics]] and [[negative thinking]], which [[David Corfield]] created yesterday.
   *  In response to Zoran immediately below, I don\'t think that we should change what works for us to fit Google.  It\'s Google\'s job to give good search results, not ours to optimise Google\'s finding us, which Google tries to prevent anyway.  That said, I agree with you about the page names, for other reasons.  (Note to all:  There is discussion [here](http://golem.ph.utexas.edu/category/2009/05/nlab_more_general_discussion.html#c023953).)

* [[Zoran Škoda]]: created [[comorphism]] (in sheaf theory); there is hard to find a sensible and comprehensive account in the literature. Note that the treatment is more general than in the usage for the case of ringed spaces. By the way, the server is very erratic tonight, and having sometimes responses delayed by 5-10 minutes. On the other hand I strongly disagree with the changes of the names of entries massively being done today by Eric: he moves infinity-category into $\infty$-category. Though this is graphically appealing, google and others put higher in search results items which have search name in the title, and the entries they index are index basically by the ascii. I want to see nlab entries high in the google search, this makes our effort more useful. Fancy graphics can be WITHIN the entry, and prefereably in this decade still not in the title. I would do the redirects in the symbol variant of the title instead!! What the others think ?

* [[Urs Schreiber|Urs]]

  * I tried to fix the query box layout at [[Tychonoff theorem]] only to find that there is apparently some software clash between the query box syntax and some symbols used. So I "rolled back". Hopefully the entry is now again in the form that [[Todd Trimble|Todd]] and [[Toby Bartels|Body]] left it. Please check.

  * started filling something into [[n-categorical physics]] just so the page looks less blank -- but didn't really have the energy or intention to produce anything of more than vaguely suggestive nature so far

* [[Zoran Škoda]] made changes to [[pure motives]]. Please do not use defined term [[algebraic spaces]] when it is not appropriate.

*  _David_ added exposition references to [[pure motive]]

* [[Urs Schreiber|Urs]]

  * added explicit description of colimits in $Set$ to [[limits and colimits by example]] -- I have a dumb question: frequently I want to use displayed math equations in a bullet list item. But more often than not when I try this the parser gets very mixed up and produces weirly formatted output -- what am I doing wrong??

# 2009-05-21 #

* [[Bruce Bartlett|Bruce]] added link to Evan Jenkins' notes of the [[Northwestern TFT Conference 2009]], and changed text+math font on the nLab to a serif theme by editing the CSS. This will only be for one day, just to create awareness of what's possible. Discussion on the [nForum](http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=23).

# 2009-05-20 #
* [[Chris Brav|Chris]] started work on section 5 of BZFN
for the journal club on geometric $\infty$-function theory.

* [[Todd Trimble|Todd]] wrote a longish reply to a query of David Roberts about tame topology over at [[nice topological space]].

*  [[Toby Bartels]] wrote [[Hausdorff space]] and [[Zorn's lemma]].

*  [[Todd Trimble]] wrote [[Tychonoff theorem]].

# 2009-05-19 #

* [[Todd Trimble|Todd]] added a bit more to [[compact space]], in particular linking back to [[quasicompact]]. There is so much one could say about compact spaces, it's quite the embarrassment of riches.

* [[Zoran Škoda]]: created [[algebraic geometry]], [[algebraic stack]], [[topological stack]]; updated [[quasicompact]] with the definition and facts about quasicompact morphisms.

* [[Urs Schreiber|Urs]]:

  * created [[Northwestern TFT Conference 2009]]

  * added cross-links between [[compact object]] and [[compact space]]

* [[Todd Trimble]] created [[compact space]]

* [[Urs Schreiber|Urs]]:

  * added a short section _Basic idea in three words_ to the beginning of [[geometric infinity-function theory]], as I noticed that this simple introductory statement was not sufficiently amplified in the existing introductory section

  * thanks to [[Toby Bartels|Toby]] for (in particular) his editorial work! it doesn't go unnoticed, is much appreciated

# 2009-05-18 #

*  [[Todd Trimble]] has also created [[uniform space]] and [[ultrafilter theorem]].

* [[Chris Brav|Chris]]:

  * Replied to Urs on [[fiber product]], suggesting that fiber products be computed using a cobar resolution and  that we should eventually make a section about derived fiber product of spaces.

* [[Urs Schreiber|Urs]]:

  * added an "Idea"-section to [[homotopy category]] and added the precise definition of the universality condition on $Q : C \to Ho(C)$

  * replied to [[Chris Brav|Chris]] at [[fiber product]]

  * expanded [[local isomorphism]]: more about sieves, more about pullbacks -- but needs polishing

  * created [[commutativity of limits and colimits]] as a place to list results such as commutativity of filtered colimits with finite limits;

  * added a further definition to [[image]], created [[coimage]] and [[strict morphism]]

# 2009-05-17 #

*  [[Todd Trimble]] wrote [[metric space]], and there was much rejoicing.

* [[Urs Schreiber|Urs]]:

  * restructured [[compact object]]

# 2009-05-16 #

*  [[Toby Bartels]]:
   *  Created [[algebra for an endofunctor]] and [[monoid object]] just to be linked to from [[algebra]], but they are very much stubs; there is related discussion at [[coalgebra]].
   *  Changed the category of [[Anders Kock]] from [people](/nlab/list/people) to [biography](/nlab/list/biography), although frankly I can\'t remember why we keep these separate.
   *  Noted exactly which limits are needed at [[power object]].
   *  Noted on [[direct product]] just how trivial the direct coproduct is.
   *  Answered Mike\'s question at [[algebraic theory]] by incorporating actual theorems from an actual reference instead of using vague handwaving in the query box, for once.

# 2009-05-15 #

* [[Bruce Bartlett|Bruce]]:

  * I created a Stylish extension for Firefox to make the edit box  bigger and wider when editing pages (I always found this annoying). To install it, install [Stylish](https://addons.mozilla.org/en-US/firefox/addon/2108) and then [click here](http://userstyles.org/styles/17934).

  * Started adding Todd's comments about compact objects in categories to the [[compact object]] page.

* [[David Corfield|David]]:

  * began [[synthetic differential geometry]] and [[analytic versus synthetic]]

* [[Urs Schreiber|Urs]]:

  * further refined the discussion of the relation to localization at [[geometric embedding]]

# 2009-05-14 #

* [[Urs Schreiber|Urs]]:

  * added some bits to [[subobject classifier]]: a short intro, the realization in presheaf topoi and a paragraph on $n$-catgorical generalizations and the interpretation of $true$ as a $-1$-category.

  * created [[power object]], which is mentioned in the alternative definition at [[topos]] --  guessed the definition from the _Axiom of power sets_ at [[Trimble on ETCS I]], but I am not really sure -- somebody please have a look and check

  * expanded and restructured [[Grothendieck topos]]

  * added what should be a detailed proof to [[geometric embedding]] that for every geometric embedding $f_* : F \hookrightarrow E$ the category $F$ is equivalent to the localization of $E$ at the morphisms that are sent by $f^*$ to isos

    * there are two possibilities here: either I am mixed up or this is somewhere in the literature. If the latter, can anyone give me a pointer to a reference that mentions this explicitly?

  * created [[geometric embedding]] -- am in the process of filling in a detailed discussion of the relation to [[localization]]

  * added a paragraph to [[localization]] describing and emphasizing the point that lots of localizations one runs into in practice are [[reflective subcategory|reflective subcategories]] or actually [[geometric embedding|geometric embeddings]]. In particular [[Bousfield localization]] presents the corresponding [[reflective (infinity,1)-subcategory]]. I am still not really satisfied with the entry [[localization]], though, I am hoping we can eventually present the conceptual basis here more clearly. After all, the perspective on sheaves and sheafification in terms of localization/geometric embedding has been shown to be the workable road to $\infty$-stacks, which, as tradition has it, are well worth pursuing in general and on an $n$Lab in particular :-) It is curious that there seems to be a cultural divide in the literature here: the book by Kashiwara-Schapira for instance amplifies sheafification as localization, which paves the road for $\infty$-stacks presented by the [[model structure on simplicial presheaves]], while the book by MacLane-Moerdijk amplifies sheafification as geometric embedding, which paves the road for the simple definition of [[(infinity,1)-sheafification]] by [[reflective (infinity,1)-subcategory]]. Lurie's book effectively gives the unified perspective, which I think is worthwhile presenting very clearly here on the $n$Lab, since it is coceptually so simple and transparent and in practice so powerful. Over.

  * added example to [[localization of a simplicial model category]]

  * added a little proposition to [[dependent product]] and a little example to [[geometric morphism]]

*  [[Tim Porter|Tim]]: I have given a partial reply to [[Urs Schreiber|Urs]] question at [[homotopy coherent nerve]].

# 2009-05-12 #

*  [[Toby Bartels]]:  An extensive rewrite and expansion of [[predicative mathematics]], including material on the non-[[constructive mathematics|constructive]] school (which rejects function sets), thanks to reading sparked by [one of Jonathan's posts](http://golem.ph.utexas.edu/category/2009/04/taming_the_boundless.html#c023753) to the Café.

* [[Urs Schreiber|Urs]]

  * created [[derived smooth manifold]], but will have to continue tomorrow

  * created [[category of local models]] and [[locally modeled monoid]]

  * expanded a bit more on the "good limits"-motivation at [[derived stack]], alongside the [blog discussion](http://golem.ph.utexas.edu/category/2009/05/journal_club_geometric_infinit_3.html#c023770)

  * added a few more details to [[generalized smooth algebra]] -- and have a question on that on the blog [here](http://golem.ph.utexas.edu/category/2009/05/journal_club_geometric_infinit_3.html#c023762)

  * added a few bits and pieces to [[derived stack]], [[ind-object in an (infinity,1)-category]], [[perfect infinity-stack]]

* [[David Corfield|David]]

  * began [[Eckmann-Hilton duality]]. Referred to it from [[duality]], but maybe that page needs some adjustment. By the way, I still don't think I have answers to questions posed [here](http://golem.ph.utexas.edu/category/2009/04/cohomology.html#c023057) and below.

  * began [[initial algebra]] and [[terminal coalgebra]].

* [[Urs Schreiber|Urs]]

  * added the coherence diagrams to [[braided monoidal category]]

  * added the enriched versions to [[representable functor]] and [[opposite category]]

# 2009-05-11 #

*  [[Toby Bartels]]:  I moved all of the <abbr title="scalable vector graphics">SVG</abbr> out of article pages and into included subpages as described at [[HowTo]].  (Note that this is supposed to be a temporary fix until we get a working automated system to include somehthing like TikZ; see [the discussion](http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=20).)

* [[Urs Schreiber|Urs]]:

  * added more details to and slightly restructured [[exact functor]]

    * in particular added a remark on and a link to "[[flat functor]]", which overlaps in content

    * I changed at [[flat functor]] the condition that $(d/F)$ be filtered to the condition that it be cofiltered. Please check that I am not hallucinating! But see for instance [[Categories and Sheaves|KashSch prop. 3.3.2]]

  * after reading it I got the idea that [[Toby Bartels|Toby]]'s latest addition to [[stuff, structure, property]] is really about higher subobject classifiers as discussed at [[generalized universal bundle]]. I added corresponding remarks, but didn't find the time to look into this very carefully.

*  [[David Corfield|David]]: Started [[locally finitely presentable category]]

*  [[Toby Bartels]]:
   *  Added a sort of logical interpretation to [[stuff, structure, property]].  (This has some links that ought to be filled out.)
   *  There\'s more work going on at [[SVG Sandbox]] and being discussed in [a Forum post](http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=20).  See also the new [[Inclusion Sandbox]].
   *  There\'s been some work recently at [[generalized element]], in response to a reader\'s question.

# 2009-05-08 #

*  [[Toby Bartels]]:  Fixed the last 'heuristic', at [[local system]], among other such fixes.  (You gotta open them up for editing and look at the source!)

* [[Urs Schreiber|Urs]]:

  * tied up the loose end at [[descent]] using the expected result that Dominic Verity was kind enough to proof on request and then confirm by private communication

* [[Andrew Stacey|Andrew]]: (I forget whether I'm supposed to add this to my earlier comment, or here, or add a word of this to each of the other entries of the day).  I've created [[SVG Sandbox]] expressly for the purpose of mucking about with SVGs to get them to look right.  My rationale is explained at the top of that page, together with some suggestions on how it might work.  The point is that one SVG can be rather large and I think that putting them in the regular Sandbox to test stuff is a bit anti-social.  Hopefully we can get stuff in the [[FAQ]] and [[HowTo]] on good ways of importing SVGs as there seem to be a few "special features".  I've shifted the recent SVG-related stuff from the original [[Sandbox]] to the [[SVG Sandbox]], but I shifted the discussion that Bruce started to the [nForum](http://www.math.ntnu.no/~stacey/Mathforge/nForum/).

  * [[Urs Schreiber|Urs]]: I believe [[Mike Shulman|Mike]] had requested that we announce each change here always on the very top of the list, even if we had earlier logs the same day with other people's logs already on top of them. Seems to be a reasonable practice if the point of this page here is to alert others of changes. Which it is. So, yes, the way you did it should be the preferred way.

* [[Urs Schreiber|Urs]]:

  * recalled [[Tim Porter]]'s comment at [[simplicial set]] and moved [[simplicial nerve of simplicial categories]] to [[homotopy coherent nerve]];

  * started expanding, polishing and reorganizing [[simplicial set]] -- still not satisfied, though.

* [[Bruce Bartlett|Bruce]]: Added discussion to [[Sandbox]] about Andrew's TikZ->SVG method. Maybe we can get good and easy graphics going soon in Instiki!

* [[Urs Schreiber|Urs]]:

  * added lots of further stuff to [[simplex category]]

* [[Andrew Stacey|Andrew]]: Finished off the heuristic shift.  Bizarrely, one page, [[local system]], comes up in the Instiki search as having "heuristic" in it but I can't find it.  The other instances of "heuristic" that are left are either correct or within discussions.

* [[Urs Schreiber|Urs]]:

  * added explicitly the description in terms of weighted (co)limits and in terms of (co)ends to [[Kan extension]]; also reorganized the existing material somewhat.

  * added the definition of composition to [[enriched functor category]];

  * thanks to [[Andrew Stacey|Andrew]] for the thing about "heuristic". I'll be aware of that in the future.

    * following [[Toby Bartels|Toby]] I made [[heuristic introduction to sheaves, cohomology and higher stacks|heuristic intro...]] a redirection to [[motivation for sheaves, cohomology and higher stacks]]

*  [[Toby Bartels]]:
   *  I split [[identity]] into [[identity morphism]] and [[identity element]].  Maybe I\'ll do the same to [[inverse]] later, but not now.
   *  More details at [[extensional relation]].

# 2009-05-07 #

*  [[Toby Bartels]]:  Reply to Andrew below:
   *  Yeah, that\'s pretty much how to do it.  Except that you mark the old page as `category: redirect` rather than as `category: delete`, since it contains edit history that we want to preserve.  (Instiki has no cool page-move feature like MediaWiki does.)  As you did, I also usually decline to change links from discussion.
   *  I would move [[heuristic introduction to sheaves, cohomology and higher stacks]] to [[motivation for sheaves, cohomology and higher stacks]], since Urs doesn\'t like [[introduction to sheaves, cohomology and higher stacks]].

* [[Andrew Stacey|Andrew]]

  * Heuristically altered records containing the word "heuristic".  The original list of records matching the search term "heuristic" is below (so anyone worried can check what I've done).  Most actually were references to [[heuristic introduction to sheaves, cohomology and higher stacks]] which obviously needs to be renamed before the other pages are changed (what's the best way to rename a page?  Is it: create a new one, copy over the content, put in a redirect, change all referring pages, mark old one for delete?  Or is there a simpler way?).  In a couple of the others the word was used in a discussion so I didn't change those.  One I even left as I thought it was (almost) correctly used!

    * [[2009 April changes]]
    * [[Categories and Sheaves]]
    * [[General Discussion]]
    * [[Grothendieck's Galois theory]]
    * [[cohomology]]
    * [[full functor]]
    * [[geometric infinity-function theory]]
    * [[heuristic introduction to sheaves, cohomology and higher stacks]]
    * [[hyperstructure]]
    * [[induced representation]]
    * [[limit]]
    * [[local system]]
    * [[sheaf]]
    * [[sheaf cohomology]]
    * [[space and quantity]]
    * [[stuff, structure, property]]
    * [[weighted limit]]
    * [[why (infinity,1)-categories?]]

* [[Urs Schreiber|Urs]]

  * as a reaction to the discussion taking place there I expanded the text at [[simplicial model for weak omega-categories]] -- also added references

# 2009-05-06 #

* [[Urs Schreiber|Urs]]

  * reacted to the discussion at [[Day convolution]] and provided the requested further details in the main entry

  * corrected the statement about the relation of $SetMod$ to $Span(Set)$ at [[distributor]] by adding the missing clause about discrete categories

  * created [[structured generalized space]]

  * created [[string theory]]

# 2009-05-05 #

* [[David Corfield|David]]:

  * began [[things to be categorified]]

*  [[Toby Bartels]]:
   *  Fixed up [[extensional relation]], although there seems to be a problem with one of the counterexamples.
   *  I also have an opinion at [[simplicial model for weak omega-categories]].

* [[Urs Schreiber|Urs]]:

  * added a pedagogical example to [[enriched functor category]]

* [[David Corfield|David]]:

  * began [[microcosm principle]]

* [[Urs Schreiber|Urs]]:

  * added details to [[enriched functor]]

  * added a bit more detail to [[closed monoidal structure on presheaves]]

  * replied at [[cohomology]]

# 2009-05-04 #

* [[Urs Schreiber|Urs]]

  * worked on [[end]]: added a section "End as equalizer" where I try to motivate the formula for the end over $V$-valued functors from the equalizer formula for limits, then give the equalizer formula for ends -- personally I find this a bit more helpful than dinatural transformations, but that is certainly just my ignorance -- I added an "Idea" and a "References" and an "Examples" section

  * added the definition to [[enriched category]] (yes, that was still "left as an exercise")

# 2009-05-03 #

*  [[Toby Bartels]]:
   *  Wrote [[FOLDS]] (and [[Michael Makkai]]), [[identity functor]], [[identity natural transformation]], [[anafunctor category]], [[identity anafunctor]], [[anabicategory]], and [[ananatural transformation]] to be linked from the below.
   *  Rewrote [[equivalence of categories]], moving one paragraph to [[Cat]] and otherwise expanding.
   *  Urs and I would like some advice from [[Tim Porter]] at [[simplicial nerve]].

* [[Urs Schreiber|Urs]]:

  * further expanded section 2 of [[geometric infinity-function theory]], which I am to "report" on next Monday in our Journal Club.

  * finally created [[simplicial nerve of simplicial categories]], but more details necessary...

  * am trying to find out, for [[A-infinity ring]] and [[E-infinity ring]] to which extent the two definitions "algebra over an $\infty$-operad" and "algebra object in a monoidal $(\infty,1)$-category" are equivalent, as one would expect...

  * created [[symmetric monoidal (infinity,1)-category]], [[commutative algebra in an (infinity,1)-category]], [[smash product of spectra]], [[associative ring spectrum]], [[A-infinity ring]], [[commutative ring spectrum]], [[E-infinity ring]]

  * expanded the intro at [[higher algebra]] a bit

  * thanks, [[Toby Bartels|Toby]], for your editorial help! Yes, right, "[[higher algebra]]" should be lower case, true.

# 2009-05-02 #

*  [[Toby Bartels]]:
   *  Disambiguated [[simplicial category]], hopefully correctly, at [[(infinity,1)-category]], [[derived stack]], and [[pretriangulated dg-category]].
   *  Wrote [[proper class]].
   *  Moved [[Higher Algebra]] to [[higher algebra]] because it *seemed* to be about the subject rather than about just Lurie\'s two papers, but I may have been wrong about that.
   *  Formatted theorems at [[descent for simplicial presheaves]] and [[descent]].
   *  Answered questions at [[biproduct]], [[comma category]], [[exponential object]], and [[context]].

# 2009-05-01 #

* [[Finn Lawler]]

  * Created [[lax 2-adjunction]], complete with spiffy PNGs.

  * Added some links at [[Gray-adjointness-for-2-categories]] to entries on concepts in the book.  Some of these are to non-existent pages like [[lax natural transformation]].  Do pages on 'elementary' stuff like this belong here on nLab, or should we add them to Wikipedia and link there?

    +--{: .query}
    [[Mike Shulman|Mike]]: If we have a page on [[category|categories]], we can certainly have a page on lax natural transformations!

    [[Jonas Frey]]: The problem about lax natural transformations is that there is no consensus about the orientation of constraints in the literature. Johnstone in the elephant and Gurski in his PhD-thesis for example use an other orientation than Leinster and Borceux in their books.

    _Toby_:  All the more reason to write an article to explain the differences!
    =--

* [[Urs Schreiber|Urs]]

  * created new top-level link list [[Higher Algebra]] -- to be filled with content...

  * considerably expanded [[(infinity,1)-category]] -- motivation was really to write [[relation between quasi-categories and simplicial categories]], but then ran out of steam

  * removed all existing logs here and archived them as [[2009 April changes]]

***

[[2008 changes|First list]] --- [[2009 April changes|Previous list]] --- [[2009 June changes|Next list]] --- [Current list](http://www.math.ntnu.no/~stacey/Mathforge/nForum/?CategoryID=5)

***

category: meta