Basic Category Theory (Cambridge Studies in Advanced Mathematics, Series Number 143)

Tl;dr: I strongly recommend this text, but if you are unsure if this book is for you, there is an open-access pdf of it on Arxiv released by the author so you can give it a look before buying. Make: The book has a nice hardcover and thicker pages which is great because I take notes in pen. In some of the diagrams the text can be small, but I’ve only noticed this when I am not wearing my glasses. If you are like me and have trouble reading pdfs, this physical copy will not disappoint. Content: I have only worked through the first few chapters but what I have read has been awesome. The exposition is straightforward but comprehensive and the examples add a lot to the discussion. To work through some of the examples and exercises, a basic grasp of topology, group theory, linear algebra, and/or ring theory are helpful. However, I would be comfortable handing this to anyone who doesn’t mind looking up a few facts. This is one of the few books I would recommend doing all of the exercises. Several of the exercises are fairly quick and round out the chapters discussion or supplement examples. I also recommend reading the foreword as it explains the author’s thought process while writing the book.

Category theory has an unfounded reputation of being very difficult. I think that may be because people start with MacLane and get scared away by how terse it is. This book is sort of the dual to MacLane-- It has amazing clarity and presentation, while not covering quite as much material. Reading it feels more like a private lecture than a textbook. If you are just reaching the point in your mathematical education where you are learning material on your own, this is a fantastic place to start. One point of caution, however-- people coming from a functional programming background should be aware that this book does NOT cover monads. However, once you are finished with it, learning about them will not take you very long.

Exactly what Robert Sievers said in his review. It's focused and well-written. With Awodey, it's often hard to tell what's really important and what's not. With Leinster, everything is important.

This is a slightly edited version of the authour's lecture notes in category theory still available from his home page. (*** Added, the 23rd February, 2016 *** The original notes are gone, and the authour says a free online version will be released soon. Thus one will be able to download the entire book for free, but perhaps the printing cost will dictate one to purchase instead.) I wrote "for ordinary students" because the intended audience are general students of mathematics who are not particularly interested in category for the sake of category. As everybody is aware, there are textbooks on category theory with established reputations: namely ones by Mac Lane and Awodey respectively. Compared to those two, Leinster's book covers somewhat less both in width and depth: for example, he has put the proof for Adjoint Functor Theorem in the appendix and merely touches upon Special Adjoint Functor Theorem without giving a precise statement and its proof. But it is much more accessible than Mac Lane and Awodey: Mac Lane's book should be titled "Category for the category theorist", while Awodey has put an emphasis on the relation between category and logic which is beyond the scope of most students of mathematics. The bottom line is, unless you specialise in a heavily category-oriented area, this is probably the only textbook on category theory you will ever need.

I don't disagree with any of the very positive reviews here. But if you're truly a beginner, let me warn you about what mathematicians mean by words like "basic", "simple", "easy introduction to", etc. Being a real beginner means: 1. You don't know anything about the subject to begin with; 2. You are trying to learn the terminology of the field by reading about it. The very first (substantive) sentences of this book say: "Our first example of a universal property is very simple. Let 1 denote a set with one element." Already, WTF!? To the beginner, 1 is a number that I learned about in elementary school. It is not a set (despite ZFC's definition, which as a beginner, I don't know about). So you glean that they're using the name "1" in some special way that you don't quite understand. You're immediately disoriented. You don't know what things you already think you know about 1 to hold onto and which to redefine for this special context. Yes, it is "mathematically legal" to introduce a new definition for an old name. You can call it anything you damn well please. And yes, calling it 1 evokes to the "essential singleness" of a singleton set. And yes, that kind of thing doesn't upset the "mathematically mature" (BTW, I've got a BS in Math from MIT). But is it wise to do so in a book for absolute beginners? Hell, no. It's not "very simple" at all for the beginner. Why cause needless confusion? And that's what we're dealing with. Many math books mean "simple", "basic", etc. only in the sense of having few prerequisites in prior knowledge of specific mathematical fields. It doesn't mean that they are easy to understand for beginners. To beginners: Don't let it stop you from reading this book. Don't say to yourself, "They tell me it's simple, so if I don't understand it, I'm too stupid or I'm not cut out for math", etc. Read carefully. Get a good math teacher to explain to you how to think about mathematical definitions. Ask "why" questions. To mathematicians who write introductory books: Think hard about what a real beginner does and does not understand. Don't sweep confusion under the rug by saying you require "mathematical maturity". Most importantly: User test it. If your teenager who likes math and took one calculus course doesn't think it's simple, it's your fault. Fix it.

La pasta es una mala impresión de la pasta dura forrada en tela, clásica de los libros de Oxford. Las páginas no están cosidas sino pegadas y temo que se desprendan con el uso. Pareciera una edición en pasta blanda a la que pusieron pastas duras de mala calidad. El contenido es hermoso.

Well-written and clear. I enjoyed reading this book and found it useful for review and ideas in general on the applications of category theory.

Great to grasp the basics of Category Theory for anyone with a bit of undergrad level math experience. As I said on the title there's a more recent and slightly corrected version of this book openly shared by the author himself online, with the .tex source file too. Still but this if you want to support the author for his work, or even just to have a nice hardcover copy.

Provides by far the most digestible introduction to category theory and covers the fundamental topics, in a very clear and concise way.

わかりやすい圏論の入門書です。電子書籍で買ったのですがまだページ表示がわからなくて論文の引用に困っています。これは著者には全く責任はありません。圏論ブームの前に一足早くお買い求めください。きっといいことがあります。