๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Categories for the Working Mathematician

โœ Scribed by Saunders Mac Lane (auth.)


Book ID
127454184
Publisher
Springer
Year
1978
Tongue
English
Weight
3 MB
Edition
2
Category
Library
City
New York
ISBN-13
9780387984032

No coin nor oath required. For personal study only.

โœฆ 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. 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.

โœฆ Subjects


K-Theory


๐Ÿ“œ SIMILAR VOLUMES


Set theory for the working mathematician
โœ Krzysztof Ciesielski ๐Ÿ“‚ Library ๐Ÿ“… 1997 ๐Ÿ› Cambridge University Press ๐ŸŒ English โš– 993 KB

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory,