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© 2006

Categories and Sheaves

Benefits

  • 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

Textbook

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 332)

Table of contents

About this book

Introduction

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.

Keywords

Category theory Homological algebra algebra sheaves stacks unbound derived categories

Authors and affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Institut de MathématiquesUniversité Pierre et Marie CurieParis Cedex 05France

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/

 

 

Bibliographic information

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)