Jacob LurieJuly 6, 2009

Princeton University PressThe book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.

Publisher

Princeton University Press

Published on

Jul 6, 2009

Pages

944

ISBN

9781400830558

Features

Best For

Language

English

Genres

Mathematics / Algebra / Abstract

Mathematics / Applied

Mathematics / Logic

Mathematics / Set Theory

Mathematics / Topology

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