Methods of Homological Algebra

  • Sergei I. Gelfand
  • Yuri I. Manin

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XX
  2. Sergei I. Gelfand, Yuri I. Manin
    Pages 1-55
  3. Sergei I. Gelfand, Yuri I. Manin
    Pages 57-138
  4. Sergei I. Gelfand, Yuri I. Manin
    Pages 139-238
  5. Sergei I. Gelfand, Yuri I. Manin
    Pages 239-290
  6. Sergei I. Gelfand, Yuri I. Manin
    Pages 291-356
  7. Back Matter
    Pages 357-374

About this book

Introduction

Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

Keywords

Cohomology Homological algebra Sheaf cohomology category theory homotopical algebra

Authors and affiliations

  • Sergei I. Gelfand
    • 1
  • Yuri I. Manin
    • 2
  1. 1.American Mathematical SocietyProvidenceUSA
  2. 2.Max Planck Institute for MathematicsBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12492-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07813-2
  • Online ISBN 978-3-662-12492-5
  • Series Print ISSN 1439-7382
  • About this book