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Category Theory (Oxford Logic Guides, 52)

Steve Awodey · 2 HN comments
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Amazon Summary
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.
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If I remember correctly, Awodey[0] has exercises like that.

[0] http://www.amazon.com/Category-Theory-Oxford-Logic-Guides/dp...

runT1ME
Awodey's does not have answers to the exercises, so it makes it hard to find out if I'm getting close or just scribbling things down...
MacLane is still the standard for working mathematicians, but for those with less background, Steve Awodey's book[1] is very good. He also has some YouTube lectures[2]. While you're on YouTube, the Catsters channel[3] has many excellent 10-minute category theory videos.

[1] http://www.amazon.com/Category-Theory-Oxford-Logic-Guides/dp...

[2]https://www.youtube.com/playlist?list=PLGCr8P_YncjVjwAxrifKg...

[3]https://www.youtube.com/channel/UC5Y9H2KDRHZZTWZJtlH4VbA

Verdex
I can second the Catsters channel. As a complete category theory newbie watching those videos was nevertheless enjoyable because of the upbeat and cheerful attitude with which the material was covered.

I actually found MacLane's book to be more approachable than Awodey's. Although I'm not sure this is good advice because it took me several years casually feeling my way through the field to start to gain an understanding into it (ie YMMV).

Interesting category theory historical fact! Checkout MacLane's wikipedia page and you will find one of his students was in fact Steve Awodey.

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