Category Theory

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 of the other fields in which the ideas are being applied. Containing clear definitions of the 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, theorems, and methods of category theory understandable to this broad readership.

Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda’s lemma; adjoints; 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 expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

Table of Contents

1 Categories

2 Abstract structures

3 Duality

4 Groups and categories

5 Limits and colimits

6 Exponentials

7 Naturality

8 Categories of diagrams

9 Adjoints

10 Monads and algebras

About the Author

Steve Awodey studied Mathematics and Philosophy at the University of Marburg (Germany) and the University of Chicago, earning his Ph.D. from Chicago under Saunders Mac Lane in 1997. He is now a Professor in the Department of Philosophy at Carnegie Mellon University. He is an active researcher in Category Theory and Logic, and has authored and co-authored numerous journal articles.