Categories for the working mathematician
Saunders Mac Lane (Author)
"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."--Jacket
xii, 314 pages : illustrations ; 25 cm.
9780387984032, 9781441931238, 0387984038, 1441931236
37928530
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
App. Foundations
Table of Standard Categories: Objects and Arrows