Barr M., Wells C. Category Theory for Computing Science

Canada.: TAC, 2012 (No. 22), — 538 p., eBook, English. (Free Published).[Reprints in Theory and Applications of Categories (TAC), No. 22, 2012]
Transmitted by Richard Blute, Robert Rosebrugh and Alex Simpson. Reprint published on 2012-09-
19. Canada, Free Publications].[Reprint with Correction, Original Published: 3rd Ed. (1st publ. 1990; 2nd, 1995). - UK.: Prentice Hall, 1998. - 538 p. - ISBN: 2-921120-31-3-6, English]Preface to the TAC reprint
This is a reprint of the final version, published by the Centre de Recherche Math ematique at the Universit e de Montr eal. We are aware of only one error, which will be corrected below. If any others are reported, we will post corrections. The error was a missing diagram in the solution to problem (4_1_4_) The problem is on page 98 and the solution on page 438.This book is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. We expound the constructions we feel are basic to category theory in the context of examples and applications to computing science. Some categorical ideas and constructions are already used heavily in computing science and we describe many of these uses. Other ideas, in particular the concept of adjoint, have not appeared as widely in the computing science literature. We give here an elementary exposition of those ideas we believe to be basic categorical tools, with pointers to possible applications when we are aware of them.
In addition, this text advocates a specfic idea: the use of sketches as a systematic way to turn nite descriptions into mathematical objects. This aspect of the book gives it a particular point of view. We have, however, taken pains to keep most of the material on sketches in separate sections. It is not necessary to read to learn most of the topics covered by the book.Preliminaries.
Categories.
Functors.
Diagrams, naturality and sketches.
Products and sums.
Cartesian closed categories.
Finite product sketches.
Finite discrete sketches.
Limits and colimits.
More about sketches.
The category of sketches.
Fibrations.
Adjoints.
Algebras for endofunctors.
Toposes.
Categories with monoidal structure.
Solutions to the exercises.