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© 2003

Methods of Homological Algebra

Book

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

  1. 1.American Mathematical SocietyProvidenceUSA
  2. 2.Max Planck Institute for MathematicsBonnGermany

Bibliographic information

  • Book Title Methods of Homological Algebra
  • Authors Sergei I. Gelfand
    Yuri I. Manin
  • Series Title Springer Monographs in Mathematics
  • 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
  • Hardcover ISBN 978-3-540-43583-9
  • Softcover ISBN 978-3-642-07813-2
  • eBook ISBN 978-3-662-12492-5
  • Series ISSN 1439-7382
  • Edition Number 2
  • Number of Pages XX, 372
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as a monograph
  • Topics Category Theory, Homological Algebra
  • Buy this book on publisher's site

Reviews

From the reviews of the second edition:

"This is the revised edition of a modern approach to homological algebra by two leading writers in the field. It is based on the systematic use of the language and technics of derived categories and derived functors. The reader has all the basic material and a lot of examples … . This book can be used by students just beginning to study homological algebra, as well as by specialists who will find there some points which have never been clarified in the literature." (Jean-Claude Thomas, Belgian Mathematical Society – Simon Stevin Bulletin, Vol. 10 (2), 2003)

"It is a pleasure to have on the desk this second edition from a new classical text in mathematics. … this text has to be seen as part of the general process of unification in mathematics." (Bernd Richter, Zentralblatt MATH, Vol. 1006, 2003)