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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.

Category theory. Homological algebra --- Toposes --- Set theory --- Logic, symbolic and mathematical --- Logic, Symbolic and mathematical --- Topoi (Mathematics) --- Categories (Mathematics) --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Mathematics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Logic, Symbolic and mathematical. --- Set theory. --- Toposes. --- Topos (mathématiques) --- Logique mathématique --- Théorie des ensembles --- Logique mathématique --- Théorie des ensembles --- Topos (mathématiques) --- Catégories (mathématiques)

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Topos theory has led to unexpected connections between classical and constructive mathematics. This text explores Lawvere and Tierney's concept of topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. A virtually self-contained introduction, this volume presents toposes as the models of theories — known as local set theories — formulated within a typed intuitionistic logic. The introductory chapter explores elements of category theory, including limits and colimits, functors, adjunctions, Cartesian closed categories, and Galois connections. Succeeding chapters examine the concept of topos, local set theories, fundamental properties of toposes, sheaves, locale-valued sets, and natural and real numbers in local set theories. An epilogue surveys the wider significance of topos theory, and the text concludes with helpful supplements, including an appendix, historical and bibliographical notes, references, and indexes.

Toposes --- Logic, symbolic and mathematical --- Set theory

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