Categories and Sheaves: An Introduction to Ind-Objects and Derived Categories (Grundlehren der mathematischen Wissenschaften)

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9783540279495: Categories and Sheaves: An Introduction to Ind-Objects and Derived Categories (Grundlehren der mathematischen Wissenschaften)
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Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

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"This book of Kashiwara and Schapira, recognized specialists in algebraic analysis, is a detailed full-scale exposition of categories, homological algebra and sheaves. These notions are presented from scratch up to the most recent (sometimes new) results ... ." (Corrado Marastoni, Mathematical Reviews, Issue 2006 k)

Synopsis:

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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9783642066207: Categories and Sheaves (Grundlehren der mathematischen Wissenschaften)

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Book Description Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany, 2005. Hardback. Condition: New. 2006 ed.. Language: English . Brand New Book ***** Print on Demand *****.Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Seller Inventory # APC9783540279495

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