Categories and Sheaves
By: Kashiwara, Masaki [author.].
Contributor(s): Schapira, Pierre [author.] | SpringerLink (Online service).
Material type:
BookSeries: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 332Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.Description: X, 498 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540279501.Subject(s): Mathematics | Category theory (Mathematics) | Homological algebra | Manifolds (Mathematics) | Complex manifolds | Mathematics | Category Theory, Homological Algebra | Manifolds and Cell Complexes (incl. Diff.Topology)DDC classification: 512.6 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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E books
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PK Kelkar Library, IIT Kanpur | Available | EBK7855 |
The Language of Categories -- Limits -- Filtrant Limits -- Tensor Categories -- Generators and Representability -- Indization of Categories -- Localization -- Additive and Abelian Categories -- ?-accessible Objects and F-injective Objects -- Triangulated Categories -- Complexes in Additive Categories -- Complexes in Abelian Categories -- Derived Categories -- Unbounded Derived Categories -- Indization and Derivation of Abelian Categories -- Grothendieck Topologies -- Sheaves on Grothendieck Topologies -- Abelian Sheaves -- Stacks and Twisted Sheaves.
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.
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