Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorMac Lane, Saunders. author
TitleCategories for the Working Mathematician [electronic resource] / by Saunders Mac Lane
ImprintNew York, NY : Springer New York : Imprint: Springer, 1978
Edition Second Edition
Connect tohttp://dx.doi.org/10.1007/978-1-4757-4721-8
Descript XII, 317 p. online resource

SUMMARY

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


CONTENT

I. Categories, Functors, and Natural Transformations -- II. Constructions on Categories -- III. Universals and Limits -- IV. Adjoints -- V Limits -- VI. Monads and Algebras -- VII. Monoids -- VIII. Abelian Categories -- IX. Special Limits -- X. Kan Extensions -- XI. Symmetry and Braiding in Monoidal Categories -- XII. Structures in Categories -- Appendix. Foundations -- Table of Standard Categories: Objects and Arrows -- Table of Terminology


Mathematics K-theory Mathematics K-Theory



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram