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A Course in Homological Algebra

  • P. J. Hilton
  • U. Stammbach

Part of the Graduate Texts in Mathematics book series (GTM, volume 4)

Table of contents

  1. Front Matter
    Pages I-IX
  2. P. J. Hilton, U. Stammbach
    Pages 1-9
  3. P. J. Hilton, U. Stammbach
    Pages 10-39
  4. P. J. Hilton, U. Stammbach
    Pages 40-83
  5. P. J. Hilton, U. Stammbach
    Pages 84-115
  6. P. J. Hilton, U. Stammbach
    Pages 116-165
  7. P. J. Hilton, U. Stammbach
    Pages 166-183
  8. P. J. Hilton, U. Stammbach
    Pages 184-228
  9. P. J. Hilton, U. Stammbach
    Pages 229-254
  10. P. J. Hilton, U. Stammbach
    Pages 255-305
  11. P. J. Hilton, U. Stammbach
    Pages 306-330
  12. Back Matter
    Pages 331-340

About this book

Introduction

In this chapter we are largely influenced in our choice of material by the demands of the rest of the book. However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. In Chapter III we begin the proper study of homological algebra by looking in particular at the group ExtA(A, B), where A and Bare A-modules. It is shown how this group can be calculated by means of a projective presentation of A, or an injective presentation of B; and how it may also be identified with the group of equivalence classes of extensions of the quotient module A by the submodule B.

Keywords

Category theory Cohomology Homological algebra Lie Topology algebra mathematics

Authors and affiliations

  • P. J. Hilton
    • 1
    • 2
  • U. Stammbach
    • 3
  1. 1.Battelle Memorial InstituteSeattleUSA
  2. 2.Department of Mathematics and StatisticsCase Western Reserve UniversityClevelandUSA
  3. 3.Mathematisches InstitutEidgenössische Technische HochschuleZurichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9936-0
  • Copyright Information Springer-Verlag New York 1971
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90033-9
  • Online ISBN 978-1-4684-9936-0
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site