Pierre Schapira: Categories and Sheaves

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Cover: 9783642066207 | Categories and Sheaves | Pierre Schapira (u. a.) | Taschenbuch | X

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Masaki Kashiwara Professor at the Rims, Kyoto University
Plenary speaker ICM 1978
Invited speaker ICM 1990
[...]

Pierre Schapira, Professor at University Pierre et Marie Curie (Paris VI)
Invited speaker ICM 1990
[...]

Zusammenfassung

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic and exhaustive 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. 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.

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	508
Reihe:	Grundlehren der mathematischen Wissenschaften
Inhalt:	x 498 S.
ISBN-13:	9783642066207
ISBN-10:	3642066208
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Schapira, Pierre Kashiwara, Masaki
Auflage:	Softcover reprint of hardcover 1st ed. 2006
Hersteller:	Springer Berlin Springer Berlin Heidelberg Grundlehren der mathematischen Wissenschaften
Maße:	235 x 155 x 28 mm
Von/Mit:	Pierre Schapira (u. a.)
Erscheinungsdatum:	12.02.2010
Gewicht:	0,762 kg