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  • © 1978

Categories for the Working Mathematician

Part of the book series: Graduate Texts in Mathematics (GTM, volume 5)

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  • ISBN: 978-1-4757-4721-8
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Softcover Book USD 74.95
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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    • Saunders Mac Lane
    Pages 1-5
  3. Constructions on Categories

    • Saunders Mac Lane
    Pages 31-53
  4. Universals and Limits

    • Saunders Mac Lane
    Pages 55-78
  5. Adjoints

    • Saunders Mac Lane
    Pages 79-108
  6. Limits

    • Saunders Mac Lane
    Pages 109-136
  7. Monads and Algebras

    • Saunders Mac Lane
    Pages 137-159
  8. Monoids

    • Saunders Mac Lane
    Pages 161-190
  9. Abelian Categories

    • Saunders Mac Lane
    Pages 191-209
  10. Special Limits

    • Saunders Mac Lane
    Pages 211-232
  11. Kan Extensions

    • Saunders Mac Lane
    Pages 233-250
  12. Symmetry and Braidings in Monoidal Categories

    • Saunders Mac Lane
    Pages 251-266
  13. Structures in Categories

    • Saunders Mac Lane
    Pages 267-287
  14. Back Matter

    Pages 289-317

About this book

Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.

Keywords

  • Adjoint functor
  • Morphism
  • addition
  • algebra
  • theorem

Reviews

From the reviews of the second edition:

“The book under review is an introduction to the theory of categories which, as the title suggests, is addressed to the (no-nonsense) working mathematician, thus presenting the ideas and concepts of Category Theory in a broad context of mainstream examples (primarily from algebra). … the book remains an authoritative source on the foundations of the theory and an accessible first introduction to categories. … It is very well-written, with plenty of interesting discussions and stimulating exercises.” (Ittay Weiss, MAA Reviews, July, 2014)

Second Edition

S.M. Lane

Categories for the Working Mathematician

"A very useful introduction to category theory."—INTERNATIONALE MATHEMATISCHE NACHRICHTEN

Authors and Affiliations

  • Department of Mathematics, University of Chicago, Chicago, USA

    Saunders Mac Lane

Bibliographic Information

  • Book Title: Categories for the Working Mathematician

  • Authors: Saunders Mac Lane

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-4721-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1978

  • Hardcover ISBN: 978-0-387-98403-2

  • Softcover ISBN: 978-1-4419-3123-8

  • eBook ISBN: 978-1-4757-4721-8

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XII, 317

  • Topics: K-Theory

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4757-4721-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 74.95
Price excludes VAT (USA)
Hardcover Book USD 74.95
Price excludes VAT (USA)