This book is intended as a text book on category theory not only for students of mathematics but also, as the author says in the preface, "for researchers and students in computer science, logic, cognitive sciences, philosophy and students in other fields that now make use of it". Very few mathematical prerequisites are expected of the reader. Illustrative examples are concentrated on various aspects of posets and monoids (e.g. the poset as a category on one side and the category of posets and their monotone maps on the other side, and analogously for monoids). No example is given from topology (even in the paragraph "Stone duality" no topology is mentioned).

The author has been giving courses on category theory at Carnegie Mellon University over the last ten years. The lecture course, based on the material in this book, consists of two 90 minute lectures every week for fifteen weeks. The author himself says that “the selection of material was easy. There is a standard core that must be included: categories, functors, natural transformations, equivalence, limits and colimits, functor categories, representables, Yoneda's lemma, adjoints, and monads. That nearly fills a course. The only 'optional' topic included here is Cartesian closed categories and the lambda-calculus, which is a must for computer scientists, logicians and linguists.” The book is written with the pedagogical mastership of a skilled teacher trying to help the reader as much as possible. This excellent textbook can be recommended to everybody who would like to learn the basis of category theory.

Reviewer:

vtr