ENGLISH

Categories for the Working Mathematician

By Saunders Mac Lane

Book information

Publisher
Springer
Year
1998
ISBN
0387984038, 9780387984032
Language
english
Format
PDF
Filesize
6 MB (6028100 bytes)
Series
Graduate Texts in Mathematics 5
Edition
Hardcover
Pages
317\331
Time added
2018-07-31 04:15:43

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.

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