Categories and Sheaves

Front Cover
Springer Science & Business Media, Oct 20, 2005 - Mathematics - 498 pages

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.

 

Contents

Introduction
1
3
The Language of Categories
9
Exercises
30
Limits
35
Filtrant Limits 71
70
Tensor Categories
93
113
117
Complexes in Additive Categories
269
Complexes in Abelian Categories
297
Derived Categories
319
Unbounded Derived Categories 347
346
Indization and Derivation
369
Grothendieck Topologies
389
Sheaves on Grothendieck Topologies 405
404
Abelian Sheaves
435

7
145
3
159
Exercises
166
9
202
Exercises
235
Stacks and Twisted Sheaves
461
References 483
482
Index
491
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About the author (2005)

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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