Abstract and Concrete Categories: The Joy of Cats (Dover Books on Mathematics) by Jiri Adamek (PDF)

Description

This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases.A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

User’s Reviews

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

⭐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.

⭐Good book

⭐It’s a little bit too much for me. Slews of definitions and symbol manipulation, little insight into the theory.

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