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＜電子ブック＞
Categories and Sheaves / by Masaki Kashiwara, Pierre Schapira
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 332)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	X, 498 p : online resource
著者標目	*Kashiwara, Masaki author Schapira, Pierre author SpringerLink (Online service)
件　名	LCSH:Algebra, Homological LCSH:Manifolds (Mathematics) FREE:Category Theory, Homological Algebra FREE:Manifolds and Cell Complexes
一般注記	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 HTTP:URL=https://doi.org/10.1007/3-540-27950-4

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