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Analyse mathématique --- Mathematical analysis. --- Analyse microlocale

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Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays. This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies.

Categories (Mathematics) --- Sheaf theory --- Algebra. --- Categories (Mathematics). --- Cell aggregation -- Mathematics. --- Electronic books. -- local. --- Geometry --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Cell aggregation --- Mathematics. --- Aggregation, Cell --- Cell patterning --- Category theory (Mathematics) --- Category theory (Mathematics). --- Homological algebra. --- Manifolds (Mathematics). --- Complex manifolds. --- Category Theory, Homological Algebra. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Cell interaction --- Microbial aggregation --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Mathematical analysis --- Sheaf theory. --- Homological algebra --- Algebra, Abstract --- Homology theory --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Catégories (mathématiques) --- Faisceaux

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Geometric quantization. --- D-modules. --- Noncommutative differential geometry. --- Poisson manifolds. --- Quantification géométrique. --- D-modules, Théorie des. --- Géométrie différentielle non commutative. --- Poisson, Variétés de.

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"D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann–Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense." [Publisher]

D-modules. --- D-modules, Théorie des. --- Modules (Algebra) --- Modules (algèbre) --- Sheaf theory. --- Faisceaux, Théorie des. --- Geometry, Algebraic. --- Géométrie algébrique.

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Fonctions de plusieurs variables complexes --- Equations aux derivees partielles sur une variete --- Categories (mathematiques) --- Categories abeliennes