Category Theory

Oxford Logic Guides #52

by Steve Awodey

This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it.
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 it assumes 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!

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

270 pages, Hardcover

First published January 1, 2006

Reviews

[Sandy Maguire]

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...

[Mark Moon]

Definitely worth a reread. I don't think I'll be using this for teaching as much anymore, as Riehl's "Category Theory in Context" and Leinster's "Basic Category Theory" will probably be better for most students.

[Sandor Molnar]

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]

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.