Categories and Sheaves - Masaki Kashiwara, Pierre Schapira

Categories and Sheaves

Buch | Softcover
X, 498 Seiten
2010 | 1. Softcover reprint of hardcover 1st ed. 2006
Springer Berlin (Verlag)
978-3-642-06620-7 (ISBN)
85,59 inkl. MwSt

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.

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/

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.

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)

Erscheint lt. Verlag 12.2.2010
Reihe/Serie Grundlehren der mathematischen Wissenschaften
Zusatzinfo X, 498 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 761 g
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte Algebra • category theory • Homological algebra • Sheaves • stacks • unbound derived categories
ISBN-10 3-642-06620-8 / 3642066208
ISBN-13 978-3-642-06620-7 / 9783642066207
Zustand Neuware
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