Category Theory in Context (Aurora: Dover Modern Math Originals)

I had planned to write this review when I finished chapter 2. By that standard, this review is premature.This is the perfect book for rejuvenating a long dormant interest in advanced mathematics. My math is decades old, and long past its best by date, but I am slowly regaining strength.If you want a good grounding in category theory, this text offers incredible value -- if and only if you read carefully and work the exercises. Let me repeat that: to garner the text's incredible value, you must read carefully, take notes, and do the problems -- all of them. I've read 37 pages, and taken 60 double sided pages of notes. This is definitely a book for grown ups.Ms. Riehl treats her readers as peers and extends every possible courtesy. Explanations are clear and complete and peppered with examples. There is an extensive bibliography (which I look forward to exploring when I recover mathematical fitness), and a complete subject index, accompanied by a notation index and an index of categories. I have never before seen an index of notation, and I find it extremely valuable. I wish that all mathematics texts had them.If you decide to take the plunge, I suggest that you include the following in your order:1. A good mechanical pencil2. Lots of lead (I find that BB is easy on the hand)3. A good, sewn in signature notebook. I like this one: https://www.amazon.com/Grid-Paper-Notebook-Hardcover-Dividers/dp/B072MVXYKS/ref=pd_rhf_ee_s_rp_c_2_0_5/140-5454927-85018684: A good eraser. Seriously, you will need it. I like these: https://www.amazon.com/STAEDTLER-Plastic-Latex-free-Age-resistant-Crumbling/dp/B00006IFAN/ref=sr_1_2Happy Mathing.

I was struggling with the "classic" category theory text by Mac Lane so I decided to give this a try. Much easier to follow and overflowing with examples that help motivate and illustrate the theory. Though I have a math background I found especially helpful that the author also draws connections to computer science as appropriate. The exercises are of appropriate difficulty and are worthwhile since many are components of the main proofs. The decision to present the Yoneda lemma immediately after establishing the basics and before doing limits, I feel is much more sensible than the "classic" order.

Best book on category I've read. (I've only read a couple of the "standard" refs).Riehl's intuition for the subject is obvious and much of her presentation seems original (to me) and more illuminating than others I've read.A lot of emphasis is placed on universal properties, which I personally really like. I think this helps to tie everything together into a coherent, deep theory centered around just a few powerful ideas.

This is a nice introduction to category theory for mathematicians in branches orthogonal to algebra, such as analysis. As a more analytically bent person, the numerous examples are very helpful for staving off my proclivity to dismiss category theory as “abstract nonsense.” Category theory has become a language of modern mathematics, so I don’t think anyone serious about math can go without some familiarity with it.

This wonderful book provides a clear and thorough exposition of the fundamentals of category theory. I particularly enjoyed how the author clarifies the central role played by representable functors. In fact, I would recommend this book over Mac Lane's classic Categories for the Working Mathematician. The book is written at the level of a graduate text in mathematics - the examples assume familiarity with algebra and algebraic topology.

Beware this is a high level math text book

I'm using this book for self-study and started out reading and working problems as I went along. It didn't work: the book is too difficult as a first text for this purpose. I do think this is a good book, but it's too advanced for a first introduction.There are some statements in the introduction to the effect that few prerequisites are required if you also have some "mathematical maturity". Don't be fooled: this is code for already knowing category theory, and some essential definitions are missing. I recommend that if you are acquiring category theory by self-study you should start with "Category Theory for the Working Mathematician," because that book does define everything with complete clarity. And don't let the title of that book scare you: it is perfectly sufficient for the beginner. Steve Awodey's book "Category Theory" is another good starting point or second reference.Essentially this is the problem: to understand basic category theory you need an unambiguous interpretations of commutative and non-commutative diagrams, abstract categories ("metacategories"), and concrete categories. Then as each auxiliary definition and tool is built up you need to understand its construction unambiguously and in its full generality. These things are all fairly simple. I'm observing that once people understand all of these things together as a "language" they enjoy the experience so much that they immediately forget how to explain the basic definitions to their readers and want to just write category theory at you. And to some extent that is a positive and promising thing.I'm hoping that once I get my basic grounding in category theory and come back to finish reading this book that the more advanced material is presented well enough that I can understand it. I expect that that will be true based on reviews by more advanced readers.

If you used her other book for a course and liked it, I guess you will like this one, too.