Abstract and Concrete Categories: The Joy of Cats (Dover Books on Mathematics) [Paperback]

Jiri Adamek (Author), Horst Herrlich (Author), George E Strecker (Author)

Book Description

ISBN-10: 0486469344 | ISBN-13: 978-0486469348 | Publication Date: August 3, 2009

This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures, offering a unifying perspective on earlier work and summarizing recent developments. Numerous examples, ranging from general to specific, illuminate the text. 1990 edition, updated 2004.

Editorial Reviews

From the Publisher

A modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises. --This text refers to an out of print or unavailable edition of this title.

Product Details

• Paperback: 528 pages
• Publisher: Dover Publications (August 3, 2009)
• Language: English
• ISBN-10: 0486469344
• ISBN-13: 978-0486469348
• Product Dimensions: 9.1 x 6.1 x 1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #902,082 in Books (See Top 100 in Books)

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7 of 9 people found the following review helpful:

4.0 out of 5 stars Easy-looking Text, June 28, 2010

By 

Pawin Vongmasa (Stanford, CA USA) - See all my reviews
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This review is from: Abstract and Concrete Categories: The Joy of Cats (Dover Books on Mathematics) (Paperback)

This book is very well typeset. It looks very attractive to read.

About the things covered, this book is pretty comprehensive on the topic of categories. However, even with numerous good examples, some more explanations on the concept will definitely be preferred. For example, Yoneda's lemma is presented here as a corollary of a result whose proof is very short. Although the proof is logically presented with clarity, it makes not much sense why someone would have thought of it in the first place.

One problem I think worth mentioning is the proof of the equivalence of three conditions about concrete reflexive subcategories. In the proof, images of morphisms (under some functors) are written the same as the morphisms themselves, making the proof difficult to follow. And because all the proofs before that one are all very clear, it raises some doubt whether this particular proof is erroneous.

That said, I really appreciate authors' intention to make the book seem easy. A lot of examples definitely are useful. I only wish that, through experience, the authors would add some suggestions on how one might think about entities under discussions. (Examples: Categories as generalized monoids => Functors as generalized monoid homomorphisms. Functors as diagrams => Natural transformations as structure-preserving diagram transformations.)

P.S. This book is available online for free but I bought it anyway.