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Categories for the Working Mathematician

  • Saunders┬áMac Lane

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Saunders Mac Lane
    Pages 1-5
  3. Saunders Mac Lane
    Pages 31-53
  4. Saunders Mac Lane
    Pages 55-78
  5. Saunders Mac Lane
    Pages 79-108
  6. Saunders Mac Lane
    Pages 109-136
  7. Saunders Mac Lane
    Pages 137-159
  8. Saunders Mac Lane
    Pages 161-190
  9. Saunders Mac Lane
    Pages 191-209
  10. Saunders Mac Lane
    Pages 211-232
  11. Saunders Mac Lane
    Pages 233-250
  12. Saunders Mac Lane
    Pages 251-266
  13. Saunders Mac Lane
    Pages 267-287
  14. Back Matter
    Pages 289-317

About this book

Introduction

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

Authors and affiliations

  • Saunders┬áMac Lane
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4721-8
  • Copyright Information Springer Science+Business Media New York 1978
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3123-8
  • Online ISBN 978-1-4757-4721-8
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site