Categories for the Working Mathematician

ISBN-10: 0387984038

ISBN-13: 9780387984032

Edition: 2nd 1978 (Revised)

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Description:

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.
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Book details

List price: $74.95
Edition: 2nd
Copyright year: 1978
Publisher: Springer
Publication date: 9/25/1998
Binding: Hardcover
Pages: 317
Size: 6.75" wide x 9.50" long x 1.00" tall
Weight: 1.430
Language: English

Preface to the Second Edition
Preface to the First Edition
Introduction
Categories, Functors, and Natural Transformations
Constructions on Categories
Universals and Limits
Adjoints
Limits
Monads and Algebras
Monoids
Abelian Categories
Special Limits
Kan Extensions
Symmetry and Braiding in Monoidal Categories
Structures in Categories
Foundations
Table of Standard Categories: Objects and Arrows
Table of Terminology
Bibliography
Index
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