Overview
- Most recent results (and sometimes beyond) are presented in an exhaustive manner from scratch to full proofs
- Gives a full treatment of unbounded derived categories with applications to sheaf theory on Grothendieck topology
Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 332)
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About this book
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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Keywords
Table of contents (20 chapters)
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Front Matter
Reviews
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)
Authors and Affiliations
About the authors
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/
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Bibliographic Information
Book Title: Categories and Sheaves
Authors: Masaki Kashiwara, Pierre Schapira
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/3-540-27950-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Hardcover ISBN: 978-3-540-27949-5Published: 20 October 2005
Softcover ISBN: 978-3-642-06620-7Published: 12 February 2010
eBook ISBN: 978-3-540-27950-1Published: 19 December 2005
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 1
Number of Pages: X, 498
Topics: Category Theory, Homological Algebra, Manifolds and Cell Complexes (incl. Diff.Topology)