Categories for the Working Mathematician (Graduate Texts in Mathematics, 5) by Saunders Mac Lane (PDF)

Description

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.

User’s Reviews

Editorial Reviews: 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 EditionS.M. LaneCategories for the Working Mathematician”A very useful introduction to category theory.”―INTERNATIONALE MATHEMATISCHE NACHRICHTEN

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The highlight of “Category Theory for the Working Mathematician” (for me at least) is The Special Adjoint Functor Theorem.Imagine you get some strange semi-pictorial message in the mail. Even if it were different the next day, you wouldn’t know because of some strange little differences in the rebuswork.So, one way to decode it is to first parse. For that you need a term algebra or derivatives from(111) Universal Algebra. (1*) (Free Semigroup)Next, you can try to get a feel for some je ne se quois invoked from specific connections to the pictorial semiotics, or strange idiosyncracies. For this you’d need two the interspatial purity of(21) Topology. (Up/Down Closed-Equal as Open Sets)But, if you really wanted your deciphered code to work, satisfy the clerks in actuary and futures, so you can pat down some conditioned unconscious response, you’d need SAFT and(12) Category Theory. (Atomic Objects Into Plurality)The Special Adjoint Functor Theorem evokes the spirit of category theory. Gleaning associations of primitive semiotics by how they interact as morphisms. With pullbacks, small limits and SAFT, you can seal the fate of semantics, anti-semantics and analects without the conscience of a heretic!

⭐I love how Saunders Mac Lane writes mathematical subject books, they are informative, clear to read and understand for me.

⭐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.

⭐The jacket is not very clean but it’s fine as the cover was laminated (I have never seen this in GTMs, probably done by the library). Notes were taken but not disturbingly. Overall beyond expected.For the content, I think we can learn category here and there, but this book is a nice whole piece that serve as good reference, especially for me as I am not very familiar with the language in alg. geo. but use results there quite often.

⭐I’m still, slowly, making my way through this book in my spare time. The sheer flexibility of many of the constructions in Category Theory is something I not only am finding beautiful but it also is helping to organize an connect ideas that I had no idea needed organizating and connecting. As a first year grad student in mathematical physics, I am extremely far from an expert on anything, but I am finding the stuff I learn from MacLane in this book to provide ample inspiration for novel questions and ponderings in my studies.On top of this, as time goes on the language of Category Theory seems to be rapidly making its way into daily mathematical parlance, so for any mathematician-in-the-making I feel like this book is a solid work that should be in his or her arsenal.

⭐Category Theory shouldn’t be this tough.I was trained as an electrical engineer, so, my math is reasonably good.However, I can’t get through this book.It is geared more to a mathematician rather than someone like me, who is a software consultant, and is trying to learn Category Theory in order to gain a deeper understanding of the programming language Haskell.

⭐Received hardcover copy of this book in perfect condition.

⭐Beautifully written book by the founder of the subject. Always a good standard and a go-to source of reference.

⭐The title of the review assumes that by “everyone” we mean “everyone with some math background”, otherwise why are you even looking at this?!How could anyone not rate this book 5 stars? It is a foundational text, with clear notation, and actually pretty accessible. 5 stars!

⭐The copy i have received is badly printed. some symbols do not show at all where they should like “o” in “g o f”. some other tiny indexes are barely visible. real pity…. to late to exchange unfortunatelly

⭐All of the text is annoying to read because of how faded it is and especially with small characters (like composition or ‘) they are usually half gone. Even the thin lines on characters are gone.

⭐I know this is *the* text on the subject but my complaint is that it could be better written. The sentences are long and just some modest editing could have made it much easier to follow.

⭐Nulla da dire sul testo: è un classico per chiunque debba lavorare con le categorie. L’unico problema è che alcuni caratteri sono sbiaditi, rendendo la lettura abbastanza difficile. Inoltre, sembra che il libro sia un down scaling di una fotocopia.

⭐

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