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Cambridge Studies in Advanced Mathematics #143
Basic Category Theory
At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal via adjoint functors, representable functors, and limits. A final chapter ties all three together. The book is suitable for use in courses or for independent study. Assuming relatively little mathematical background, it is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations. Copious exercises are included.
190 pages, Hardcover
First published May 19, 2014
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Displaying 1 - 6 of 6 reviews
September 29, 2016
Start here! Surely the best of its kind, next to Riehl's forthcoming 'Category Theory in Context', which covers a little more terrain. But I really appreciate how short this volume is and without sacrificing an inch of clarity. It's just what it says on the tin, going up to the general adjoint functor theorem. Now I feel well equipped to read more advanced literature...
July 30, 2016
Will obviously need a re-read, but very much enjoyed the prose of this textbook! It's definitely how I would like to write something if/when I did write something.
February 10, 2020
Very clear, linear, with many guiding examples.
July 30, 2025
Perhaps the introductory book on category theory for self-study. 11/10, will definitely recommend to anybody curious about the subject, and even to those who are not (yet).
Sure, it doesn't really cover monads or Kan extensions or other advanced topics, but what it covers instead (and what's much more important) is the intuition behind why things are defined or work out a certain way. Where other books go dryly as "Here's a new abstraction. Definition. Theorem. Proof. Rinse, repeat.", this one goes to great lengths to explain why a piece of abstraction makes sense, and how it fits into the overall picture, and how to think about it.
Basic Category Theory also doesn't skip steps — a huge plus for self-study, where there's nobody around to confirm you've figured the missing steps correctly.
Ah, and the exercises are good. Just the right complexity level for an intro book, I think.
Sure, it doesn't really cover monads or Kan extensions or other advanced topics, but what it covers instead (and what's much more important) is the intuition behind why things are defined or work out a certain way. Where other books go dryly as "Here's a new abstraction. Definition. Theorem. Proof. Rinse, repeat.", this one goes to great lengths to explain why a piece of abstraction makes sense, and how it fits into the overall picture, and how to think about it.
Basic Category Theory also doesn't skip steps — a huge plus for self-study, where there's nobody around to confirm you've figured the missing steps correctly.
Ah, and the exercises are good. Just the right complexity level for an intro book, I think.
April 10, 2025
I think this is the first time I completely read a Math book and do (most of) the exercises. Since I was first introduced to Category Theory ten years ago, I've always found the topic obtuse and frustrating, yet deeply fascinating. Each time I tried to understand what I was assured was a pristine view of Mathematics, I only found obscurity. I think this book is a superb attempt to dissipate that fog: it is clear-cut and insightful. Delicious.
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Displaying 1 - 6 of 6 reviews