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Categories

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  • © 1972

Overview

Authors:
  1. Horst Schubert

    1. Mathematisches Institut, Universität Düsseldorf, Germany

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Table of contents (21 chapters)

  1. Front Matter

    Pages N1-XI
    Download chapter PDF

  2. Categories

    • Horst Schubert
    Pages 1-5

  3. Functors

    • Horst Schubert
    Pages 5-16

  4. Categories of Categories and Categories of Functors

    • Horst Schubert
    Pages 16-24

  5. Representable Functors

    • Horst Schubert
    Pages 24-32

  6. Some Special Objects and Morphisms

    • Horst Schubert
    Pages 32-36

  7. Diagrams

    • Horst Schubert
    Pages 37-45

  8. Limits

    • Horst Schubert
    Pages 45-62

  9. Colimits

    • Horst Schubert
    Pages 62-69

  10. Filtered Colimits

    • Horst Schubert
    Pages 69-81

  11. Setvalued Functors

    • Horst Schubert
    Pages 81-96

  12. Objects with an Algebraic Structure

    • Horst Schubert
    Pages 96-110

  13. Abelian Categories

    • Horst Schubert
    Pages 110-123

  14. Exact Sequences

    • Horst Schubert
    Pages 123-139

  15. Colimits of Monomorphisms

    • Horst Schubert
    Pages 139-152

  16. Injective Envelopes

    • Horst Schubert
    Pages 152-166

  17. Adjoint Functors

    • Horst Schubert
    Pages 166-188

  18. Pairs of Adjoint Functors between Functor Categories

    • Horst Schubert
    Pages 188-220

  19. Principles of Universal Algebra

    • Horst Schubert
    Pages 220-256

  20. Calculus of Fractions

    • Horst Schubert
    Pages 256-291
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Keywords

About this book

Categorical methods of speaking and thinking are becoming more and more widespread in mathematics because they achieve a unifi­ cation of parts of different mathematical fields; frequently they bring simplifications and provide the impetus for new developments. The purpose of this book is to introduce the reader to the central part of category theory and to make the literature accessible to the reader who wishes to go farther. In preparing the English version, I have used the opportunity to revise and enlarge the text of the original German edition. Only the most elementary concepts from set theory and algebra are assumed as prerequisites. However, the reader is expected to be mathe­ to follow an abstract axiomatic approach. matically sophisticated enough The vastness of the material requires that the presentation be concise, and careful cooperation and some patience is necessary on the part of the reader. Definitions alway precede the examples that illuminate them, and it is assumed that the reader is familiar with some of the algebraic and topological examples (he should not let the other ones confuse him). It is also hoped that he will be able to explain the con­ cepts to himself and that he will recognize the motivation.

Authors and Affiliations

  • Mathematisches Institut, Universität Düsseldorf, Germany

    Horst Schubert

Bibliographic Information

  • Book Title: Categories

  • Authors: Horst Schubert

  • DOI: https://doi.org/10.1007/978-3-642-65364-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1972

  • Softcover ISBN: 978-3-642-65366-7Published: 11 November 2011

  • eBook ISBN: 978-3-642-65364-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XIII, 385

  • Additional Information: Original German edition published in two volumes in the series: Heidelberger Taschenbücher

  • Topics: Algebra

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