Category Theory

Oxford Logic Guides #52

by Steve Awodey

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.

Genres: Mathematics, Logic, Textbooks, Computer Science, Nonfiction, Algebra, Science

311 pages, Paperback

First published January 1, 2006

Reviews

[Sandy Maguire · Rating 2 out of 5]

Went through this book at a rate of one paragraph per week, and even that was too fast. If you're not a graduate-level mathematics student, don't even consider it. My reading group and I have switched to Bartosz Milewski's Category Theory for Programmers.

https://bartoszmilewski.com/2014/10/2...

[Sandor Molnar · Rating 5 out of 5]

The definitive starting point

So, if you are as into category theory as I am, I'd suggest to go through this one first. Clear, understandable, containing loads of examples and exercises to grasp the basics.

After this you may embark on Saunders' book. After all, Awodey was a doctoral student of Saunders'.

[Andrew · Rating 3 out of 5]

I find Category Theory really tough, but this filled in some of the missing pieces. My copy contains a lot of scribbles in the margins when I grasped a concept.