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Categories for the Working Mathematician (Graduate Texts in Mathematics) (Englisch) Gebundene Ausgabe – 1. Oktober 1998

3.0 von 5 Sternen 3 Kundenrezensionen

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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


"Categories for the Working Mathematician" provides 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. The book 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 characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and expoitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them.

The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.

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Von untitled am 5. November 2013
Format: Gebundene Ausgabe
This book is very well written.
It does not lack examples to illustrate the theory although some knowledge of advanced mathematics (by advanced I mean for example group theory) is required to understand them.
But as I see it this is nothing negative. After all the book is titled "Categories for the Working Mathematician" and not "Categories for Everyone".
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Format: Kindle Edition Verifizierter Kauf
Die Kindle-Ausgabe enthält ab Abschnitt IV.1 (Monads) zahlreiche Stellen, wo statt einer Formel nur "image" steht. Sie ist daher in weiten Bereichen **unbrauchbar**. Hoffentlich wird dies schnell korrigiert!
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Von Ein Kunde am 4. Juli 2000
Format: Gebundene Ausgabe
I read this due to its odd title. It is fairly easy to understand. It assumes that you have very little previous knowledge of the subject. For me it just wasn't that useful. Perhaps I was hindered by the fact that I'm not a working mathematician. If you are a mthematics student it is probably a worthwhile read. If not, go for something else.
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Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: 4.2 von 5 Sternen 13 Rezensionen
58 von 61 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen One of the great books in mathematics 24. September 2000
Von Colin McLarty - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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 von 55 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen A Classic 3. Juli 2004
Von Jason Schorn - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
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 von 52 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Definitely a grad text 23. Juli 2001
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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.
24 von 26 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Simply Great 5. Januar 2008
Von J. Wiley - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
Have you ever tried reading Descartes' "Geometry"? It's not a good place to learn about coordinate geometry. I tried. This was almost 10 years ago, but I still remember it pretty well. Ok, so maybe the experience was even a bit traumatic.

Usually when someone works out a theory, it takes a fresh perspective (or two, or ... you get it) to really digest it, and come up with a reasonable way of teaching it to newcomers. It's less evident nowadays, with improved communications technology and such, but people aren't exactly turning to Grothendieck's expositions as their intro to his geometry either. Mac Lane is an exception.

This book seems completely inapproachable. The title is scary. The topic is scary. Open to a random page and try to judge its accessibility: scary. Well, here's the real story: you need to know algebra through modules, and it'd be nice if this algebra background introduced "universals" like abelianization or free modules in a way that involved the diagrams and the unique mappings you get from the given ones. If this stuff makes any sense, you can read this book. It's not that scary. If you're up to the challenge, you might even enjoy it. This is actually my favorite book.

Here's the approach that I feel worked well for me:

- gloss over the set-theoretic foundations at first. Make sure you know the proper class/set and large/small category distinctions, but don't dwell on them much.

- focus on the examples that are familiar, but read through the others too. Mac Lane uses tons of examples to suit a variety of backgrounds, and his presentation is so clear that the theory can often explain the examples.

- trust the author. It may seem like product or comma categories deserve fuller treatment with more motivation. No. Let Mac Lane's 'minimalism' infect your thinking: it's no more complicated than what's on those pages. Make sure you *know* what's there, and you will come to *understand* the material as it is fleshed out through exercises or later writing.

The last point has been the most important for me. This book has been a great lesson in clear thinking, which is of extreme importance in mathematics. Why? It's complicated enough!
16 von 20 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Classic and worth it 12. August 2003
Von Pietro Braione - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
It is difficult to make understand what "is" category theory. Is it a foundational discipline? Is it a discipline studying homomorphisms between algebras? Is it nonsense? Well, in my opinion this book does not help in gaining this kind of understanding. But all the stuff I read which have been written with that purpose in mind did not have any success - perhaps because I am not a mathematician, or perhaps because some concepts in category theory are really too abstract for anyone to give "an intuition" of them (you still can with functors and natural transformations, but try with adjointness...). This said, I found the book wonderful: Every concept is presented neatly. I use it as a reference each time I want a clear and rigorous definition of a concept. Sometimes this rigour helped me in gaining the famous intuition behind the concept.
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