a functorial semantics for multi algebras and partial algebras with applications to syntax multi algebras allow for the modelling of nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results we propose a functorial presentation of various categories of multi algebras and partial algebras analogous to the classical presentation of algebras over a signature as cartesian functors from the algebraic theory over to set we introduce two different notions of theory over a signature both having a structure weaker than cartesian and we consider functors from them to rel or pfn the categories of sets and relations or partial functions respectively next we discuss how the functorial presentation provides guidelines when choosing syntactical notions for a class of algebras and as an application we argue that the natural generalization of usual terms are conditioned terms for partial algebras and term graphs for multi algebras

conformal operators on forms and detour complexes on einstein manifolds for even dimensional conformal manifolds several new conformally invariant objects were found recently invariant differential complexes related to but distinct from the de rham complex these are elliptic in the case of riemannian signature the cohomology spaces of these conformally stable form spaces that we may view as spaces of conformal harmonics operators that generalise branson s q curvature global pairings between differential form bundles that descend to cohomology pairings here we show that these operators spaces and the theory underlying them simplify significantly on conformally einstein manifolds we give explicit formulae for all the operators concerned the null spaces for these the conformal harmonics and the cohomology spaces are expressed explicitly in terms of direct sums of subspaces of eigenspaces of the form laplacian for the case of non ricci flat spaces this applies in all signatures and without topological restrictions in the case of riemannian signature and compact manifolds this leads to new results on the global invariant pairings including for the integral of q curvature against the null space of the dimensional order conformal laplacian of graham et al

differential invariants and curved bernstein gelfand gelfand sequences we give a simple construction of the bernstein gelfand gelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry this method permits us to define the additional structure of a bilinear differential cup product on this sequence satisfying a leibniz rule up to curvature terms it is not associative but is part of an a algebra of multilinear differential operators which we also obtain explicitly we illustrate the construction in the case of conformal differential geometry where the cup product provides a wide reaching generalization of helicity raising and lowering for conformally invariant field equations

subcomplexes in curved bgg sequences bgg sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries for locally flat geometries the resulting sequences are complexes but in general the compositions of the operators in such a sequence are nonzero in this paper we show that under appropriate torsion freeness and or semi flatness assumptions certain parts of all bgg sequences are complexes several examples of structures including quaternionic structures hypersurface type cr structures and quaternionic contact structures are discussed in detail in the case of quaternionic structures we show that several families of complexes obtained in this way are elliptic

tractor calculi for parabolic geometries parabolic geometries may be considered as curved analogues of the homogeneous spaces g p where g is a semisimple lie group and p c g a parabolic subgroup conformal geometries and cr geometries are examples of such structures we present a uniform description of a calculus called tractor calculus based on natural bundles with canonical linear connections for all parabolic geometries it is shown that from these bundles and connections one can recover the cartan bundle and the cartan connection in particular we characterize the normal cartan connection from this induced bundle connection perspective we construct explicitly a family of fundamental first order differential operators which are analogous to a covariant derivative iterable and defined on all natural vector bundles on parabolic geometries for an important subclass of parabolic geometries we explicitly and directly construct the tractor bundles their canonical linear connections and the machinery for explicitly calculating via the tractor calculus

existence of natural and projectively equivariant quantizations we study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold m to that aim we make use of the thomas whitehead approach of projective structures and construct a casimir operator depending on a projective cartan connection we attach a scalar parameter to every space of differential operators and prove the existence of a quantization except when this parameter belongs to a discrete set of resonant values

restriction categories ii partial map classification an algebraic characterization of monads which are abstract partial map classifiers is provided without the assumption that the categories of total maps possess products by an abstract partial map classifier we mean a monad whose kleisli category is a full subcategory of a partial map category wherein the induced comonad classifies partial maps in the usual sense a construction of the corresponding actual partial map classifier from an abstract one is described and conditions for an abstract partial map classifier to be a real one are provided the paper uses the notion of a restriction category developed in earlier work and the characterization of these as full subcategories of partial map categories

geometric structures as deformed infinitesimal symmetries a general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries specifically this model consists of a lie algebroid equipped with an affine connection compatible with the lie algebroid structure the curvature of this connection vanishes precisely when the structure is locally symmetric this model generalizes cartan geometries a substantial class to the intransitive case simple examples are surveyed and corresponding local obstructions to symmetry are identified these examples include foliations riemannian structures infinitesimal g structures symplectic and poisson structures

projective compactness and conformal boundaries for complete affine manifolds we treat a recently introduced general notion of compactification based on the projective differential geometry i e geodesic path data of the given connection this involves a real parameter called the order of projective compactness for volume preserving connections this order is a measure of asymptotic volume growth via the levi civita connection this concept applies to complete pseudo riemannian metrics so projective compactness provides a geometrically motivated alternative to conformal compactification we study the fundamental links between interior geometry and the embedding of the boundary hypersurface at infinity and develop the tools that describe the induced geometry on this boundary we prove that a pseudo riemannian metric which is projectively compact of order two admits a certain asymptotic form this form was known to be sufficient for projective compactness so the result establishes that it provides an equivalent characterization from a projectively compact connection on m one obtains a projective structure on the compactified manifold with boundary overline m we show this induces a possibly degenerate conformal structure on the boundary hypersurface partial m we prove that in the case of metrics which are projectively compact of order two this boundary structure is in fact always non degenerate we also prove that in this case the metric is necessarily asymptotically einstein in a natural sense finally a non degenerate conformal boundary geometry gives rise to a conformal standard tractor bundle on the boundary endowed with a canonical linear connection and we explicitly describe these in terms of the projective data of the interior geometry

higher symmetries of the conformal powers of the laplacian on conformally flat manifolds a r g gratefully acknowledges support from the royal society of new zealand via marsden grant nos 06 uoa 029 and 10 uoa 113 j s was supported by the max planck institute fur math ematik in bonn and by the grant agency of the czech republic under the grant no p201 12 g028

relative bgg sequences ii bgg machinery and invariant operators abstract for a real or complex semisimple lie group g and two nested parabolic subgroups q p g we study parabolic geometries of type g q associated to the group p we introduce the classes of relative natural bundles and of relative tractor bundles and construct some basic invariant differential operators on such bundles we define a rather weak notion of compressability for operators acting on relative differential forms with values in a relative tractor bundle then we develop a general machinery which converts a compressable operator to an operator on bundles associated to completely reducible representations on relative lie algebra homology groups applying this machinery to a specific compressable invariant differential operator of order one we obtain a relative version of bgg bernstein gelfand gelfand sequences all our constructions apply in the case p g producing new and simpler proofs in the case of standard bgg sequences we characterize cases in which the relative bgg sequences are complexes or even fine resolutions of certain sheaves and describe these sheaves we show that this gives constructions of new invariant differential operators as well as of new subcomplexes in certain curved bgg sequences the results are made explicit in the case of generalized path geometries

tail recursion through universal invariants abstract tail recursive constructions suggest a new semantics for datatypes which allows a direct match between specifications and tail recursive programs the semantics focuses on loops their fixpoints invariants and convergence convergent models of the natural numbers and lists are examined in detail and under very mild conditions are shown to be equivalent to the corresponding initial algebra models

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

a linear mixed effects model with heterogeneity in the random effects population abstract this article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed effects model it shows that if the distribution of random effects is a finite mixture of normal distributions then the random effects may be badly estimated if normality is assumed and the current methods for inspecting the appropriateness of the model assumptions are not sound further it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then compare the fitted model with the gaussian model all of this is illustrated on two practical examples

bent cable regression theory and applications we use the so called bent cable model to describe natural phenomena that exhibit a potentially sharp change in slope the model comprises two linear segments joined smoothly by a quadratic bend the class of bent cables includes as a limiting case the popular piecewise linear model with a sharp kink otherwise known as the broken stick associated with bent cable regression is the estimation of the bend width parameter through which the abruptness of the underlying transition may be assessed we present worked examples and simulations to demonstrate the regularity and irregularity of bent cable regression encountered in finite sample settings we also extend existing bent cable asymptotics that previously were limited to the basic model with known linear slopes of 0 and 1 practical conditions on the design are given to ensure regularity of the full bent cable estimation problem if the underlying bend segment has nonzero width under such conditions the least squares estimators are shown to be co

bayesian bent cable growth mixture tobit models for longitudinal data with skewness and detection limit application to aids studies this paper presents a new bayesian methodology for identifying a transition period for the development of drug resistance to antiretroviral drug or therapy in hiv aids studies or other related fields estimation of such a transition period requires an availability of longitudinal data where growth trajectories of a response variable tend to exhibit a gradual change from a declining trend to an increasing trend rather than an abrupt change we assess this clinically important feature of the longitudinal hiv aids data using the bent cable framework within a growth mixture tobit model to account for heterogeneity of drug resistance among subjects the parameters of the bent cable growth mixture tobit model are also allowed to differ by subgroups subpopulations of patients classified into latent classes on the basis of trajectories of observed viral load data with skewness and left censoring the proposed methods are illustrated using real data from an aids clinical study copyright 2016 john wiley sons ltd

unfolding semantics of graph transformation several attempts have been made of extending to graph grammars the unfolding semantics originally developed by winskel for safe petri nets but only partial results were obtained in this paper we fully extend winskel s approach to single pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of semi weighted graph grammars and the category of prime algebraic domains which factorises through the category of occurrence grammars and the category of asymmetric event structures for general possibly nonsemi weighted single pushout grammars we define an analogous functorial concurrent semantics which however is not characterised as an adjunction similar results can be obtained for double pushout graph grammars under the assumptions that nodes are never deleted

a new maximum likelihood algorithm for piecewise regression abstract this paper presents a piecewise regression method for continuous models containing max or min operators or both this method does not require knowledge of the zone in which a shift in regimes occurs moreover it allows the application of analytical derivatives to maximize the likelihood function which greatly simplifies the estimation of the model the method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables

algebraic approach to single pushout graph transformation abstract the single pushout approach to graph transformation interprets a double pushout transformation rule of the classical algebraic approach which consists of two total graph morphisms as a single partial morphism from the left to the right hand side the notion of a double pushout diagram for the transformation process can then be substituted by a single pushout diagram in an appropriate category of partial morphisms it can be shown that this kind of transformation generalizes the double pushout framework hence the classical approach can be seen as a special and very important case of the new concept it can be reobtained from the single pushout approach by imposing an application condition on the redices which formulates the gluing conditions in the new setting on the other hand single pushout transformations are always possible even if the gluing conditions for the redex are violated the simpler structure of a direct transformation one pushout diagram instead of two simplifies many proofs hence the whole theory for double pushout transformations including sequential composition parallel composition and amalgamation can be reformulated and generalized in the new framework some constructions provide new effects and properties which are discussed in detail

an equational notion of lifting monad we introduce the notion of an equational lifting monad a commutative strong monad satisfying one additional equation valid for monads arising from partial map classifiers we prove that any equational lifting monad has a representation by a partial map classifier such that the kleisli category of the former fully embeds in the partial category of the latter thus equational lifting monads precisely capture the equational properties of partial maps as induced by partial map classifiers the representation theorem also provides a tool for transferring nonequational properties of partial map classifiers to equational lifting monads it is proved using a direct axiomatization of kleisli categories of equational lifting monads this axiomatization is of interest in its own right

construction of boundary invariants and the logarithmic singularity of the bergman kernel in which case the coefficients aj are expressed by the weyl invariant theory in terms of the riemannian curvature tensor and its covariant derivatives the bergman kernel s counterpart of the time variable t is a defining function r of the domain by f1 and bs the formal singularity of k at a boundary point p is uniquely determined by the taylor expansion of r at p thus one has hope of expressing modulo on 1 r and modulo o r in terms of local biholomorphic invariants of the boundary provided r is appropriately chosen in f3 fefferman proposed to find such expressions by reducing the problem to an algebraic one in invariant theory associated with cr geometry and indeed expressed modulo on 19 r invariantly by solving the reduced problem partially the solution in f3 was then completed in beg to give a full invariant expression of modulo on 1 r but the reduction is still

conformally invariant powers of the laplacian a complete nonexistence theorem conformally invariant operators and the equations they determine play a central role in the study of manifolds with pseudo riemannian riemannian conformai and related structures this observation dates back to at least the very early part of the last century when it was shown that the equations of massless particles on curved space time exhibit conformai invariance in this setting a key operator is the con formally invariant wave operator which has leading term a pseudo laplacian the riemannian signature variant of this operator is a fundamental tool in the yam abe problem on compact manifolds here one seeks to find a metric from a given conformai class that has constant scalar curvature recently it has become clear that higher order analogues of these operators viz conformally invariant operators on weighted functions i e conformai densities with leading term a power of the laplacian have a central role in generating and solving other curvature prescription problems as well as other problems in geometric spectral theory and mathematical physics 2 5 15 in the flat setting the existence of such operators dates back to 16 where it is shown that on 4 dimensional minkowski space for k g n 1 2 the kth power of the flat wave operator ak acting on densities of the appropriate weight is invariant under the action of the conformai group more generally if w denotes the space of conformai densities of weight uigl then on a flat conformai manifold of dimension n 3 and any signature there exists for each k e n a unique conformally invariant operator

an extension theorem for conformal gauge singularities we analyze conformal gauge or isotropic singularities in cosmological models in general relativity using the calculus of tractors we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics

yang mills detour complexes and conformal geometry working over a pseudo riemannian manifold for each vector bundle with connection we construct a sequence of three differential operators which is a complex termed a yang mills detour complex if and only if the connection satisfies the full yang mills equations a special case is a complex controlling the deformation theory of yang mills connections in the case of riemannian signature the complex is elliptic if the connection respects a metric on the bundle then the complex is formally self adjoint in dimension 4 the complex is conformally invariant and generalises to the full yang mills setting the composition of two operator yang mills complexes for anti self dual yang mills connections via a prolonged system and tractor connection a diagram of differential operators is constructed which when commutative generates differential complexes of natural operators from the yang mills detour complex in dimension 4 this construction is conformally invariant and is used to yield two new sequences of conformal operators which are complexes if and only if the bach tensor vanishes everywhere in riemannian signature these complexes are elliptic in one case the first operator is the twistor operator and in the other sequence it is the operator for einstein scales the sequences are detour sequences associated to certain bernstein gelfand gelfand sequences

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

invariants and calculus for projective geometries an understanding of the local invariants is essential in any study of a differential geometry with local structure in his ground breaking paper parabolic invariant theory in complex analysis f2 charles fefferman sought to describe the local scalar invariants of cr geometries one of fefferman s objectives was to describe the asymptotic expansion of the bergman kernel for a strictly pseudoconvex domain in c n in a similar manner to the asymptotic expansion of the heat kernel for riemannian manifolds as in abp he was partially successful in his endeavour but ran into severe technical difficulties since then the invariant theory programme has extended to include other parabolic geometries such as conformal and projective geometry see gr for a chronicle of this as well as an explanation of the close relationship between these structures parabolic geometries have as their fiat model a homogeneous space g p where g is semi simple and p is a parabolic subgroup previous attempts to describe the invariants of parabolic geometries have involved two steps one of these is a problem in the representation theory of the appropriate parabolic subgroup p since fefferman s pioneering work much progress has been made on such algebraic problems and related geometric problems on the fiat models g p in particular a much simpler approach and extension of fefferman s algebraic results have been found by bailey eastwood and graham begr some remaining questions in their article were solved by bailey and gover in bgo results from the projective case have proved an invaluable guide in dealing with the conformal and cr problems indeed begr and bgo are based

the decomposition of global conformal invariants iv a proposition on local riemannian invariants abstract this is the fourth in a series of papers where we prove a conjecture of deser and schwimmer regarding the algebraic structure of global conformal invariants these are defined to be conformally invariant integrals of geometric scalars the conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant a divergence and of the chern gauss bonnet integrand the present paper lays out the second half of this entire work the second half proves certain purely algebraic statements regarding local riemannian invariants these were used extensively in the first two papers in this series see alexakis 2007 2009 2 3 these results may be of independent interest applicable to related problems

restriction categories i categories of partial maps given a category with a stable system of monics one can form the corresponding category of partial maps to each map in this category there is on the domain of the map an associated idempotent which measures the degree of partiality this structure is captured abstractly by the notion of a restriction category in which every arrow is required to have such an associated idempotent categories with a stable system of monics functors preserving this structure and natural transformations which are cartesian with respect to the chosen monics form a 2 category which we call mcat the construction of categories of partial maps provides a 2 functor par mcat cat we show that par can be made into an equivalence of 2 categories between mcat and a 2 category of restriction categories the underlying ordinary functor par r0 mcat 0 ca t0 of the above 2 functor par turns out to be monadic and from this we deduce the completeness and cocompleteness of the 2 categories of m categories and of restriction categories we also consider the problem of how to turn a formal system of subobjects into an actual system of subobjects a formal system of subobjects is given by a functor into the category slat of semilattices this structure gives rise to a restriction category which via the above equivalence of 2 categories gives an m category this m category contains the universal realization of the given formal subobjects as actual subobjects

modelling environments in call by value programming languages in categorical semantics there have traditionally been two approaches to modelling environments one by use of finite products in cartesian closed categories the other by use of the base categories of indexed categories with structure each requires modifications in order to account for environments in call by value programming languages there have been two more general definitions along both of these lines the first generalising from cartesian to symmetric premonoidal categories the second generalising from indexed categories with specified structure to categories in this paper we investigate environments in call by value languages by analysing a fine grain variant of moggi s computational calculus giving two equivalent sound and complete classes of models one given by closed freyd categories which are based on symmetric premonoidal categories the other given by closed categories

a category theoretic characterization of functional completeness abstract functional languages are based on the notion of application programs may be applied to data or programs by application one may define algebraic functions and a programming language is functionally complete when any algebraic function f x1 xn is representable i e there is a constant a such that f x1 xn a x1 xn combinatory logic is the simplest type free language which is functionally complete in a sound category theoretic framework the constant a may be considered as an abstract godel number for f when godel numberings are generalized to principal morphisms in suitable categories by this models of combinatory logic are categorically characterized and their relation is given to lambda calculus models within cartesian closed categories finally the partial recursive functionals in any finite higher type are shown to yield models of combinatory logic

bayesian semiparametric mixture tobit models with left censoring skewness and covariate measurement errors common problems to many longitudinal hiv aids cancer vaccine and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time varying covariates with measurement errors there has been relatively little work published simultaneously dealing with these features of longitudinal data in particular left censored data falling below a limit of detection lod may sometimes have a proportion larger than expected under a usually assumed log normal distribution in such cases alternative models which can account for a high proportion of censored data should be considered in this article we present an extension of the tobit model that incorporates a mixture of true undetectable observations and those values from a skew normal distribution for an outcome with possible left censoring and skewness and covariates with substantial measurement error to quantify the covariate process we offer a flexible nonparametric mixed effects model within the tobit framework a bayesian modeling approach is used to assess the simultaneous impact of left censoring skewness and measurement error in covariates on inference the proposed methods are illustrated using real data from an aids clinical study

categories of partial maps abstract this paper attempts to reconcile the various abstract notions of category of partial maps which appear in the literature first a particular algebraic theory p categories is introduced and a representation theorem proved this gives the authors a coherent framework in which to place the various other definitions both algebraic theories and theories which make essential use of the poset enriched structure of partial maps are discussed proofs of equivalence are given where possible and counterexamples where known the paper concludes with brief sections on the representation of partial maps and on partial algebras

conformally invariant differential operators on minkowski space and their curved analogues this article describes the construction of a natural family of conformally invariant differential operators on a four dimensional pseudo riemannian manifold included in this family are the usual massless field equations for arbitrary helicity but there are many more besides the article begins by classifying the invariant operators on flat space this is a fairly straightforward task in representation theory best solved through the theory of verma modules the method generates conformally invariant operators in the curved case by means of penrose s local twistor transport

higher symmetries of the laplacian we identify the symmetry algebra of the laplacian on euclidean space as an explicit quotient of the universal enveloping algebra of the lie algebra of conformal motions we construct analogues of these symmetries on a general conformal manifold

growth mixture modeling with non normal distributions a limiting feature of previous work on growth mixture modeling is the assumption of normally distributed variables within each latent class with strongly non normal outcomes this means that several latent classes are required to capture the observed variable distributions being able to relax the assumption of within class normality has the advantage that a non normal observed distribution does not necessitate using more than one class to fit the distribution it is valuable to add parameters representing the skewness and the thickness of the tails a new growth mixture model of this kind is proposed drawing on recent work in a series of papers using the skew t distribution the new method is illustrated using the longitudinal development of body mass index in two data sets the first data set is from the national longitudinal survey of youth covering ages 12 23 years here the development is related to an antecedent measuring socioeconomic background the second data set is from the framingham heart study covering ages 25 65 years here the development is related to the concurrent event of treatment for hypertension using a joint growth mixture survival model

laplacian operators and q curvature on conformally einstein manifolds a new definition of canonical conformal differential operators p k k 1 2 with leading term a kth power of the laplacian is given for conformally einstein manifolds of any signature these act between density bundles and more generally between weighted tractor bundles of any rank by construction these factor into a power of a fundamental laplacian associated to einstein metrics there are natural conformal laplacian operators on density bundles due to graham jenne mason sparling gjms it is shown that on conformally einstein manifolds these agree with the p k operators and hence on einstein manifolds the gjms operators factor into a product of second order laplacian type operators in even dimension n the gjms operators are defined only for 1 k n 2 and so on conformally einstein manifolds the p k give an extension of this family of operators to operators of all even orders for n even and k n 2 the operators p k are each given by a natural formula in terms of an einstein metric but they are not natural conformally invariant operators in the usual sense they are shown to be nevertheless canonical objects on conformally einstein structures there are generalisations of these results to operators between weighted tractor bundles it is shown that on einstein manifolds the branson q curvature is constant and an explicit formula for the constant is given in terms of the scalar curvature as part of development conformally invariant tractor equations equivalent to the conformal killing equation are presented

restriction categories as enriched categories restriction categories were introduced as a simple equational axiomatisation for categories of partial maps such as those which arise in the foundations of computability theory a restriction structure on a category is given by an operation obeying four simple axioms that assigns to each morphism of the category an endomorphism of its domain to be thought of as the partial identity representing the degree of definition in this paper we show that restriction categories can be seen as a kind of enriched category this allows their theory to be studied by way of the enrichment unlike most enrichments ours is based not on a monoidal category but rather a weak double category in the sense of grandis pare and provides from a purely mathematical perspective an example of such an enrichment arising in nature beyond exhibiting restriction categories as enriched categories we show that varying the base of this enrichment also allows the important notions of join and range restriction category to be understood in the same manner

equivariant quantizations for ahs structures abstract we construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles associated to irreducible representations for a so called ahs structure outside of a finite set of critical or resonant weights this procedure gives rise to a quantization which is intrinsic to this geometric structure in particular this provides projectively and conformally equivariant quantizations for arbitrary symbols on general curved projective and conformal structures

partiality cartesian closedness and toposes presentation equationnelle des categories de morphismes partiels avec etablissement systematique des rapports entre ces structures et les classiques structures totales