Categories for the Working Mathematician

Saunders Mac Lane

ISBN 10: 0387900357 / ISBN 13: 9780387900353

Published by Springer, 1971

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Bibliographic Details

• Title: Categories for the Working Mathematician
• Publisher: Springer
• Publication Date: 1971
• Language: English
• ISBN 10: 0387900357
• ISBN 13: 9780387900353
• Binding: Hardcover
• Edition: 4th Edition
• Condition: new

About this title

Synopsis

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. Mac Lane attempted to settle an ambiguity in usage for the terms epimorphism and monomorphism by introducing the terms epic and monic, but the distinction is not in common use.

Review

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