Elementary Categories, Elementary Toposes: 21 (Oxford Logic Guides) - Softcover

It has the virtue of bringing together a great deal of basic material which is otherwise scattered about in research texts and articles. (Studia Logica)

A comprehensive introduction to elementary category theory and elementary topos theory . . . The book is well written . . . Ideal as an introduction for a researcher who wants to understand some of the more advanced material on the connection between category theory and logic. (Computing Review, February 1997)

This 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 theoretic foundations. It works with key notions 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 constriction 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.