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Title: Categories for the Working Mathematician (2nd Ed)(Graduate Texts in Mathematics, 5) by Saunders Mac Lane, Saunders MacLane, F. W. Gehring, P. R. Halmos ISBN: 0-387-98403-8 Publisher: Springer Verlag Pub. Date: December, 1998 Format: Hardcover Volumes: 1 List Price(USD): $64.95 |
Average Customer Rating: 4 (5 reviews)
Rating: 4
Summary: Classic and worth it
Comment: 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.
Rating: 4
Summary: OK, but not great
Comment: This book is a fairly good introduction to the ideas of category theory by one of the creators of the field. Unfortunately, the book is sometimes sort of confusing, and doesn't give many as many examples as I would like. Category theory (while it has become a field in its own right), is really a way of thinking about mathematics. The way you learn a way of thinking is by working out examples & doing excersizes, but this book doesn't provide as many connections to other areas of math as it should.
I don't think that this book was really intended "for the working mathematician," but rather for someone with some independent interest in category theory.
Rating: 4
Summary: Definitely a grad text
Comment: 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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Title: Basic Category Theory for Computer Scientists (Foundations of Computing) by Benjamin C. Pierce ISBN: 0262660717 Publisher: MIT Press Pub. Date: 07 August, 1991 List Price(USD): $23.00 |
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Title: Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext) by S. Mac Lane, I. Moerdijk, Saunders MacLane ISBN: 0387977104 Publisher: Springer Verlag Pub. Date: October, 1994 List Price(USD): $69.95 |
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Title: Conceptual Mathematics : A First Introduction to Categories by F. William Lawvere, Stephen Hoel Schanuel ISBN: 0521478170 Publisher: Cambridge University Press Pub. Date: 09 October, 1997 List Price(USD): $42.00 |
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Title: Algebra by Serge Lang ISBN: 038795385X Publisher: Springer Verlag Pub. Date: 08 January, 2002 List Price(USD): $69.95 |
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Title: An Introduction to Homological Algebra by Charles A. Weibel, B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak ISBN: 0521559871 Publisher: Cambridge University Press Pub. Date: 27 October, 1995 List Price(USD): $37.00 |
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