Toposes and local set theories: an introduction

The author introduces Lawvere and Tierney's concept of topos theory, a striking development in category theory that unites a number of important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topos theory has led to the forging of surprising new links between classical and constructive mathematics. Bell presents toposes as the models of theories--the so-called local set theories--formulated within a typed intuitionistic logic.