Category Theory (Oxford Logic Guides) (英語) ペーパーバック – 2010/8/13
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Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership.
Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists!
This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.
The book is well organised and very well written. The presentation of the material is from the concrete to the abstract, proofs are worked out in detail and the examples and the exercises spread throughout the text mark a pleasant rhythm for its reading. In all, Awodey's Category Theory is a very nice and recommendable introduction to the subject. (Pere Pascual, EMS Newsletter)商品の説明をすべて表示する
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。
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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 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 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.