Category Theory (Oxford Logic Guides)

Steve Awodey is, by all accounts, an excellent researcher in the field of category theory. Sadly, his abilities as a textbook writer are not of the same order. I will admit that category theory by its very nature is a difficult subject to teach. Although the basic notions are fairly straightforward, the applications of these notions are so numerous, and the level of abstraction climbs so high so quickly, that writing a good CT textbook would be a challenge for the most gifted textbook writer. Awodey is not that writer, and this book is only going to be useful to you if you are an advanced undergraduate or graduate student in mathematics with a good background in abstract algebra. In other words, it's like most CT textbooks. What's most annoying is that the author claims that the book is intended to be accessible to readers without this background, such as computer scientists (like me), linguists, cognitive scientists, and philosophers. Nothing could be further from the truth. There is absolutely no way that this book is suitable for such an audience. I couldn't get through the first chapter. The writing style is wildly, wildly uneven; there are stretches that are extremely lucid and comprehensible, but then the author drops in a bunch of advanced material, seemingly unaware of the fact that by doing so he's just lost his intended audience. Also, much of the book reads like notes the author jotted down just before a lecture. You can see in many cases that just a little more focused explanation could have really helped the exposition, but it isn't there. There are numerous notes to the reader, like suggesting that some theorem should be proved by the reader (generally indicated with just the word "proof!" in parentheses).I think that this book can be useful in two cases: first, as I mentioned before, if you are a math undergraduate or graduate student with a good background in abstract algebra, and second, if you learn the material elsewhere and need a quick refresher of things you already know. I wish that the author could team up with someone with greater didactic skill and expand this book out to the length it would need to be in order to fulfill its stated mission (which would probably double the length). In that case, it would really be a valuable book.

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.

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!

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.

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

Very solid, goes nicely with the Simmons book.

There are very few books that explain this topic clearly. This is about the only one I have come across, and even this one has mistakes in it, and some of the definitions are not as clear as they should be. Steve Awodey has told me he will be making corrections in his next edition. Meanwhile, this is still probably the best out there, and is not as expensive as most.

Best book on CT, nice print to

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.

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！

非常に丁寧に書かれており、著者の意図する読者層（非数学専攻者）に対して、十分な内容および思考法の教授に成功しているように見受けられた。終わり３章の証明部分はやや急ぎ足の感があり、説明が簡素すぎるが、それもそれでいい思考訓練になったように思われる。マックレーンの『圏論の基礎』と比べると、レベルは同程度であるが、数学の例を引き合いに出して概念を説明しようとする傾いの強いその本と比べ、本書はそのような制約をまったく設けていない。つまり、圏論の基本事項をマックレーンの本のレベルまで理解するには、この本でも足りる。もし、この本の抽象度に抵抗を覚えるようなら、H.Simmonsの「Introduction to Categoru Theory」(Cambridge University Press)を勧める。