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Categories and Sheaves

  • Masaki Kashiwara
  • Pierre Schapira

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

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

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-27950-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-27949-5
  • Online ISBN 978-3-540-27950-1
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site