Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any other fields in which the ideas are being applied. Containing clear definitions of essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas and methods of category theory understandable to a broad readership.
Although assuming few mathematical prerequisites the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories, functors categories, representables, Yoneda's lemma, adjoints, and monads. An extra topic of Cartesian closed categories and the lambda-calculus is also provided-a must for computer scientists, logicians and linguists.
This second edition contains numerous revisions to the original text, including expanded exposition, revised and elaborated proofs, additional diagrams, corrected typographical errors and an entirely new section on monoidal categories. Nearly one hundred new exercises have also been added, many with solutions, to make the book more useful as both a course text and for self-study.