- 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: 4.1 out of 5 stars See all reviews (12 customer reviews)
- Amazon Best Sellers Rank: #373,384 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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Top Customer Reviews
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.
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.
A startling demonstration presented in this book is that Cantor's Diagonal Argument in generalized form not only proves that there are infinite different levels of infinity, but also Godel's Incompleteness Theorem! Also contained is a convincingly appropriate abstraction of the characteristic function of any subobject with respect to any object it is contained in (in any sufficiently rich category). In other words, mappings in the context of a chosen category with domain X and a particular codomain Omega can correspond exactly with all objects contained within X. The latest Edition elaborates on this notion of parthood as well as introduces adjoint functors.
Lawvere is one of the developers of topos theory, where he found an axiomatization of the category of sets.
The last 2 sections are an introduction to topoi and logic. One key fact seems to be missing which caused me some perplexing: In the category of subobjects, 2 subobjects A and B has A > B if A includes B. Thus, the relation ">" creates a partial order amongst the subobjects. If A > B and B < A, then A = B, thus inducing an equivalence class, denoted by [A]. This is the reason why the subobject classifier has internal structure (different "shades" of truth values).
Also, the relation of topology to logic is analogous to the relation of classical propositional logic to the Boolean algebra of sets, with the sets replaced by open sets in topological space.
I've only read the 1st edition. The 2nd edition's first part is the same as the 1st edition, with additional advanced topics at the very end.
Most Recent Customer Reviews
For what I think of as a student review of Conceptual Mathematics textbook, please see