Customer Reviews

Topos Theory (London Mathematical Society Monographs, 10)

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You understand topos theory when you understand this book. I cannot say the same of any other.

Mac Lane and Moerdijk SHEAVES IN GEOMETRY AND LOGIC is a beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. Both those authors have a rare gift for conveying an insider's view of the subject from the start. My own book ELEMENTARY CATEGORIES, ELEMENTARY TOPOSES goes quickly and simply to the key ideas (if I say so myself). Barr and Wells TOPOSES, TRIPLES, AND THEORIES uses the most efficient tools to get at the central theorems.

But no other book goes as concisely and comprehensively to all the aspects of toposes as this one. Category theory, algebra, logic, arithmetic, geometry, and cohomology all come in, in a well chosen perspective. This book is hard to read in places, especially at the start. It cannot serve alone as an introduction unless you are really gifted. But it remains the best single text on the subject.

Johnstone has a three-volume set on the current state of topos theory due to appear later this year. It may well become the standard reference. But it will not replace this book.

This book, printed in 1978, is still an essential, I would say, unavoidable, part of a toposopher education. You have to read it right after S. MacLane's "Categories for the Working Mathematician". I have read the book three times.