Masaki Kashiwara, Pierre Schapira

Categories and Sheaves (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 498
• Erscheinungstermin: 19. Dezember 2005
• Englisch
• ISBN-13: 9783540279501
• Artikelnr.: 44122513

Autorenporträt

Masaki Kashiwara Professor at the Rims, Kyoto University Plenary speaker ICM 1978 Invited speaker ICM 1990 http://www.kurims.kyoto-u.ac.jp/~kenkyubu/kashiwara/

Pierre Schapira, Professor at University Pierre et Marie Curie (Paris VI) Invited speaker ICM 1990 http://www.math.jussieu.fr/~schapira/

Inhaltsangabe

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.

Rezensionen

From the reviews: "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)