Elementary Categories, Elementary Toposes (Oxford Logic Guides, 21) by Colin McLarty (PDF)

Description

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

User’s Reviews

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 About the Author Colin McLarty is at Case Western Reserve University, Cleveland, Ohio.

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

⭐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.

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