This page is to record the reference:
Categories for the Working Mathematician
Graduate Texts in Mathematics 5
Springer (1971, second ed. 1997)
which is a classical textbook on category theory.
The iconic title probably refers to the declared ambition of demonstrating the prevalence of examples of adjoint functors occurring throughout mathematics:
[p. 2:] “Adjoints, as we shall see, occur throughout mathematics.”
[p. 103:] “The multiple examples, here and elsewhere, of adjoint functors tend to show that adjoints occur almost everywhere in many branches of Mathematics. It is the thesis of this book that a systematic use of all these adjunctions illuminates and clarifies these subjects.”
See also:
Saunders MacLane (notes by E. Cooper): Lectures on category theory, Bowdoin Summer School (1969)
Wikipedia, Categories for the Working Mathematician
and the list of category theory textbooks here.
Contents
The original edition has the following chapters:
I. Categories, functors, and natural transformations
on the basic notions of categories, functors and natural transformations
II. Constructions on categories
on forming opposite categories, product categories, functor categories, comma categories, free categories and the (very large) category of categories.
III. Universals and limits
on universal constructions and limits
IV. Adjoints
V. Limits
VI. Monads and algebras
on monads and algebras over a monad
VII. Monoids
VIII. Abelian categories
IX. Special limits
X. Kan extensions
The 2nd edition was published in 1997 with two additional chapters:
XI. Symmetry and braidings in monoidal categories
on braided and symmetric monoidal categories
also monoidal functors, strict monoidal categories and the braid group
XII. Structures in categories
on internal categories, simplicial nerves, 2-categories/bicategories, the 2-category of categories, crossed modules and 2-groups
Last revised on April 4, 2025 at 12:14:01. See the history of this page for a list of all contributions to it.