- Hardcover: 326 pages
- Publisher: Springer; 2nd ed. edition (Sep 25 1998)
- Language: English
- ISBN-10: 0387984038
- ISBN-13: 978-0387984032
- Product Dimensions: 23.4 x 15.6 x 2.6 cm
- Shipping Weight: 621 g
- Average Customer Review: 4.0 out of 5 stars See all reviews (7 customer reviews)
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Amazon Bestsellers Rank:
#118,075 in Books (See Top 100 in Books)
- #15 in Books > Science > Mathematics > Geometry & Topology > Algebraic Geometry
- #44 in Books > Science > Mathematics > Logic
- #89 in Books > Professional & Technical > Professional Science > Mathematics > Geometry & Topology
- See Complete Table of Contents
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Product Details |
Product Description
Review
Second Edition S.M. Lane Categories for the Working Mathematician "A very useful introduction to category theory."—INTERNATIONALE MATHEMATISCHE NACHRICHTEN
Book 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.
Inside This Book
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First Sentence
Category theory starts with the observation that many properties of mathematical systems can be unified and simplified by a presentation with diagrams of arrows. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Category theory starts with the observation that many properties of mathematical systems can be unified and simplified by a presentation with diagrams of arrows. Read the first page
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Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most helpful customer reviews
5.0 out of 5 stars
A Classic,
By
This review is from: Categories for the Working Mathematician (Hardcover)
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.
3.0 out of 5 stars
You may not need this unless you major in category theory.,
By A Customer
This review is from: Categories for the Working Mathematician (Hardcover)
I entirely agree with the reviewer Lucas Wilman.As a book by the creator of category theory, it has extensively incorpoated relevant items. However I don't think this is a *must read" unless you major in the subject: you will seldom need more than what is covered in a typical homological algebra course. My inmpression is this book should be entitled "Categories for the starting/working category theorists".
4.0 out of 5 stars
Classic and worth it,
By Pietro Braione (Milano, MI Italy) - See all my reviews
This review is from: Categories for the Working Mathematician (Hardcover)
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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