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Categories for the Working Mathematician (Graduate Texts in Mathematics), by Saunders Mac Lane
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An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
- Sales Rank: #1165262 in eBooks
- Published on: 2013-04-17
- Released on: 2013-04-17
- Format: Kindle eBook
Review
From the reviews of the second edition:
“The book under review is an introduction to the theory of categories which, as the title suggests, is addressed to the (no-nonsense) working mathematician, thus presenting the ideas and concepts of Category Theory in a broad context of mainstream examples (primarily from algebra). … the book remains an authoritative source on the foundations of the theory and an accessible first introduction to categories. … It is very well-written, with plenty of interesting discussions and stimulating exercises.” (Ittay Weiss, MAA Reviews, July, 2014)
Second Edition
S.M. Lane
Categories for the Working Mathematician
"A very useful introduction to category theory."―INTERNATIONALE MATHEMATISCHE NACHRICHTEN
Most helpful customer reviews
58 of 61 people found the following review helpful.
One of the great books in mathematics
By Colin McLarty
This book is a classic. Clearly written, drawing on a vast number of different applications and motivations for the subject. Eilenberg and Mac Lane created category theory and this book is alive with the very style of thought Mac Lane brought to it in the first place. It is obvious that Mac Lane wrote each page, and each exercise, with a view of the whole book in mind. He starts with the very basics, assuming indeed that you know nothing of category theory. He goes on to adjunctions, limits, the adjoint functor theorems, monads (triples), monoidal categories, Abelian cateories, Kan extensions, higher dimensional categories, and categorical foundations. It is a masterpiece and one of the great books in mathematics.
52 of 55 people found the following review helpful.
A Classic
By Jason Schorn
Well, let us think about this a little bit...You want to learn Category theory, whether for some course or just for the fun of it, and now where do you turn in order to learn the necessary concepts. If you are a mathematician and have some experience, then you turn to the masters, the originators of the given subject and read their work. Sure, being the founder of a given subject does not imply that you are a good expositor and hence are capable of revealing the necessary concepts for the beginner-allow me to inform that Mac Lane is indeed as good as an expositor as he was a mathematician. For any doubters, I point you to the only other text you should read on Category theory, namely, "Category Theory" by Horst Herrlich and compare this text with Mac Lane's. Aside from that, and with respect to the text, for most beginners or interested readers I would suggest the following outline: Read 1.1-6; 2.1-3 & 8 possibly 2.4; all of 3; as for 4 skip section 3; 5.1-5; all of 8. Then, dependent upon your desires and or focus as well as your mathematical ability, it should become obvious which of the remaining topics should be read. Finally, the only other source I would recommend for learning Category theory can be found on-line using the keyword 'Awodey'. Anyways, Enjoy and good luck.
46 of 52 people found the following review helpful.
Definitely a grad text
By A Customer
This book is extraordinarily well written. It covers the necessary topics in a concise, orderly manner. HOWEVER, it presumes a substantial amount of knowledges concerning various algebraic/abstract structures in the field of mathematics. If you already have had experience with such structures, and are simply looking to understand them from a different perspective - this is the book for you. However, if you have limited knowledge with regards to advanced math (ie - grad level math) then try the book 'Arrows, Structures and Functors: The Categorical Imperative' by Manes and Arbib. This introduces the reader gradually to simple algebraic structures, monoids, groups, metric spaces, topological spaces, and the categories that can be built around them.
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