Elementary Categories, Elementary Toposes (Oxford Logic Guides) (Paperback)

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Editorial Reviews

Review

"An exceptionally clearly written and wide-ranging introduction to category and topos theory. . . . packed with things interesting to the expert, yet presented in a manner intelligible to the beginner. . . . contains a wealth of thought-provoking exercises." --Journal of Symbolic Logic
"Provides a first introduction to the theory of categories and functors, and to topos theory. McLarty manages to cover a considerable range of topics in a clear and elegant fashion, thus giving these readers a good first impression of what the subject is about. McLarty's perspicuous treatment provides a good first introduction." --Mathematical Reviews

Product Description

The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout, rather than beginning with set theoretical foundations. It works with key concepts such as Cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. The intended readership consists of graduate-level students in mathematics, computer science, logic, and category theory.

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Product Details

• Paperback: 280 pages
• Publisher: Oxford University Press, USA (February 1, 1996)
• Language: English
• ISBN-10: 0198514735
• ISBN-13: 978-0198514732
• Product Dimensions: 9.1 x 6 x 0.7 inches
• Shipping Weight: 14.9 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #1,418,872 in Books (See Bestsellers in Books)

• This item is part of The Oxford Logic Guides Series.

Customer Reviews

Most Helpful Customer Reviews

9 of 10 people found the following review helpful:

4.0 out of 5 stars Very good if you need no slack, October 27, 2004

By	HC Mitchell "Chett" (Elkhart IN USA) - See all my reviews

I've been working my way through McLarty's book off and on for several months now. It is a tremendously clear and well-organized book, and you can learn a lot from it. HOWEVER: it is a "math book" in the strictest sense of the word. Exposition is kept to a bare minimum, and you have to actually work your way through the material (AND the exercises, since many of the definitions are given in them) in order to learn anything. He could have easier doubled or tripled the amount of exposition and still have produced a lean, mean textbook. This is a really good book if you need to learn category theory and you already know why. The only extensive example is a short chapter on group theory. After reading his article on category theory in the Routledge encyclopedia of philosophy I expected rather more in the way of theorizing. Be that as it may: everything you need to know about categories and toposes is in here, and nothing else. The best math book I've read in a long time.