Categories for the Working Mathematician
Graduate texts in mathematics, Springer
is a classical textbook on category theory. See also
The original edition has the following chapters
The 2nd edition was published in 1997 with two additional chapters:
XI. Symmetry and braidings in monoidal categories
XII. Structures in categories
Categories Work is the standard reference for category theory, and we may often cite it here. Almost all of its terminology is widely adopted, although its approach to foundations (one Grothendieck universe) is not as widely used (see discussion at nForum).