Categories and Sheaves (Grundlehren der mathematischen Wissenschaften)
1 edition
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Word Count
124,250 words, Guess
Page Count
497 pages
Physical Format
Hardcover
Identifiers
- Open LibraryOL9055765M
- ISBN-139783540279495
- ISBN-103540279490
- OCLC Control Number61703264
- OCLC Control Numbercategoriessheave00kash
and 3 more
- Library of Congress Control Number2005930329
- LibraryThing5118288
- Goodreads3674515
Classifications
- LCCQA169 .K37 2006
Description
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.
Subjects
Topics
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