- Paperback: 404 pages
- Publisher: Cambridge University Press; 2 edition (August 31, 2009)
- Language: English
- ISBN-10: 1107654165
- ISBN-13: 978-0521719162
- ASIN: 052171916X
- Product Dimensions: 7 x 1 x 10 inches
- Shipping Weight: 1.8 pounds (View shipping rates and policies)
- Average Customer Review: 13 customer reviews
- Amazon Best Sellers Rank: #391,954 in Books (See Top 100 in Books)
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Conceptual Mathematics: A First Introduction to Categories 2nd Edition
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"This outstanding book on category theory is in a class by itself. It should be consulted at various stages of one's mastery of this fundamental body of knowledge."
George Hacken, reviews.com
Conceptual Mathematics introduces the concept of category to beginning students, general readers, and practicing mathematical scientists based on a leisurely introduction to the important categories of directed graphs and discrete dynamical systems. The expanded second edition approaches more advanced topics via historical sketches and a concise introduction to adjoint functors.
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As others have mentioned, the books seems like it might be quite simple, near the beginning. At first, given my lack of familiarity with category theory, this book made me wonder if category theory was the study of the consequences of associativity of composition laws, as that's a bit of a recurring theme in this book. And speaking of composition laws, if one wants to come up with a list of prerequisites for this book (or to start reading it, at least), I'd dare say that a familiarity with the composition of functions might be all you really need. That said, I should say this: I recently took a first pass at Rotman's Intro to Algebraic Topology and, after reading his discussion of Brouwer's fixed point theorem, I went back to Lawvere/Schanuel to revisit their section of the same topic, but still didn't feel clear about the Lawvere/Schanuel version after re-reading that section. (Rotman, on the other hand, I found quite easy to understand.) So while one could start this book with minimal prerequisites, I don't expect to feel like I'd understood it all, any time soon (and I'm well past the minimal prerequisites I just offered). And that's sort of a drawback -- the difficultly level of the book doesn't exactly scale smoothly, once you're into the latter half or so of the book. But that's probably my only criticism, as I find the discussion-driven parts of the book generally quite lucid and insightful.
It is exactly what it says on the label: a first introduction to category theory, by one of the founders of the field. Lawvere simply imho does an exemplary job of teaching a different way of thinking about math and logic: this is how it is supposed to be done.
Not a simple read, but far gentler and more intuitive than the others. Uses illustration's and even at times an informal conversational style to highlight the concepts.
It does use proofs, and even asks you to do them using proper notation. But the notation is reasonable, and the proofs logical, and can be skipped altogether if desired.
I might like it to get to be shorter or get to the point quicker. You really do need to start at the beginning and work through the chapters. For the abstract groundwork laid by earlier chapters is essential to understanding the latter ones.
Sure, it could be better. It could be clearer and have even better illustrations. But a survey of the alternatives reveals this author's love for the topic and so clearly shines above similar works, that I give it a 5 star rating.
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For what I think of as a student review of Conceptual Mathematics textbook, please see