Category Theory (Oxford Logic Guides)

This book is excellent for students with a basic knowledge of group/linear algebra, general topology and type theory, or any combination of these. Some abstract mathematics is a must unless you have a good teacher to guide you through the book. I am currently a third year undergrad majoring in maths and computer science, and so far I have found this book incredibly enjoyable and enlightening. It is orders of magnitude more accessible than MacLane's Categories for the Working Mathematician, and yet it manages to illuminate the topic in a precise, deep and thought provoking way. It has helped me to draw abstract connections and recognise deep patterns that I had previously been totally ignorant of, and I'm only a quarter of the way through the book so far. It has inspired me to start a reading group on the subject of Category Theory, and now I even want to do research in this field!

This book is good for somebody with Mathematical training (group theory, basic topology, etc) but who is not a professional Mathematician. I have enjoyed working through the book and seeing how often abstract structures from different theories that seem vaguely similar can be described as the same structure in different categories. This book might be tough for a "general audience", and I'm not sure I'm learning anything practical. But it is far more accessible than Saunders and MacLane, and much deeper and more interesting than the typical "Category for Computer Scientists" book. For me, it's just right.

I picked up the elephant book and didn't have a strong enough background in category theory. This book is a great introduction with complete proofs! Great for the self learner.

This book is an excellent and kind introduction to category theory. This theory is a very interesting approach to the foundations of mathematics as well as finding the interesting connections between its various branches.

Let me start off by saying: I highly recommend this book to any undergraduate math major with a background in algebra (a bit of topology would help as well). This is easily the most comprehensible book on the subject while still retaining the rigor that will satisfy most of those interested in graduate level mathematics. I cannot say, however, that I would recommend this book to any non-math person (viz. someone who doesn't know abstract algebra). If you are a computer science major or are anyone else interested in category theory, I would suggest "Category Theory for the Sciences" by Spivak. The only problem with that book is that it does not get very far. In fact most of the content in that book is covered in the first chapter of Awodey's, but it is a very easy book. Now, I do have some problems with this book (Awodey's) as it is. It much easier than MacLane, which can be a brutal read for those who are not a graduate student or are not equivalently mature. However, too much is left to the reader. I'm not trying to claim that leaving important (or tedious) proofs to the reader is malpractice, in fact it's a very beneficial thing. However Awodey does it too often and in inconvenient times. For example, he will list about four or five examples of something, for which he will take up an entire page to explain the first couple, but then the next few are halfway complete or left entirely to the reader. I don't quite see the point in this as he could have, just as easily, put these verification exercises in the section labeled "exercises". This would allow the reader to more fluidly read through the chapter without constantly stopping and verifying tedious claims. One more thing, and this is simply my opinion, I think he should have gone one chapter further and taught the basics of monoidal categories. Given that monoidal categories are the central focus of (nearly all) contemporary category theory (i.e. topos theory, representation theory, enriched categories, etc.), a basic, working knowledge of this would greatly benefit the readers. And, I do think Awodey can do a nice job of simplifying the complexity of monoidal categories as it is a very difficult topic.Unfortunately, the best alternative, which is not a great one mind you, is MacLane's text. Overall this book is great, I just have a few problems with it. I still highly recommend it. Edit: The second edition of this book actually does contain a section on monoidal categories. My mistake for assuming from the first edition.

This is just right, and a perfect companion to Mac Lane.

I read the first two chapters of the book and found the presentation and exercises very good. However, in the process of reading (the softcover version) the book began to slowly fall apart, with page after page becoming unbound. I found it ironic that in studying the contents of the book which helps unify all of mathematics, the book itself began to become unraveled and disheveled, and certainly contributed to my decision to suspend reading. Now I've decided to resume my studies, but have switched the Mac Lane's hardcover book which costs half the price Awodey's hardc, over version and so far has offered a clearer presentation. Well written but terrible binding.

Very solid, goes nicely with the Simmons book.

Das Produkt gefällt mir sehr. Ich habe das gekauft, weil ich das brauche fur mein Studie. Ich denke nicht das es das beste Buch für Category Theory is.

スティーヴ・アウディの講演は何度か聞いたことがあり、明快でわかりやすいので感心した。そこで、懸案の圏論の独習のため、この教科書、第2版を買って、全体の筋をざっと確認（それができるように、各章の冒頭に短い要約があって行き届いている）、最初の2章ほどを読んでみた。第1章を読んだだけで全体の質が予想できるような、明快でわかりやすい記述である。特筆すべき事は、抽象的な定義だけで済ませるのではなく、すぐに続けて、読者がある程度知っていそうな数学や論理学などの分野から、その定義に当てはまる実例がいくつも紹介されて、定義の意味がつかみやすいように親切な工夫がされていること。 また、圏論（カテゴリー理論）とは一体何を目指しているのか、という本質的な問いにも、実にわかりやすい、しかも手短な言明がズバリと付け加えられており、「あ、なるほど」と感心させる。圏論とは、"structure-preserving transformation" を特徴づけ、その条件を満たすような構造を明らかにするもの。"Transformation"とはあるものを別のものに移し替える函数 function といってもよい。函数、関係が主役で、関係づけられる対象は何でもいいのだ。そのため、一般の理論のように「しかじかの対象がどのように振る舞うか」を解明するもの、と見当をつけると、圏論のポイントを誤解してしまう。哲学系では「カテゴリー」というとカント的な分類概念を連想してしまいがちだが、そうではなく「関係づける函数、関係そのもの」が主役となるのである。10章に渡る記述にも、大きな筋書きがあって、９，10章の山場に向かう様子が最初に予告されている。読み進むのが楽しみである。なお、本書には邦訳もあるが、英語が苦手でない限り、できるだけ、わかりやすい英語で書かれた原書を読むことをおすすめする。日本語訳がまずければ、読む楽しみも半減してしまうという危惧がある！

This book is your best friend if you want to learn category theory. And probably the only book with exercises and solutions. Also have a look on videos of Steve Awodey on Youtube that are excellent.

Totalmente accesible para no matemáticos sin tener que renunciar al rigor. Contiene muchos ejemplos para conectar con gente de diferentes áreas (lógica, teoría de grupos, lambda calculus, etc.) y muchos ejercicios resueltos. Muy didáctico.

Best book on CT, nice print to