Higher Topos Theory (AM-170) PDF
By:Jacob Lurie
Published on 2009-07-06 by Princeton University Press
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The 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.
This Book was ranked at 25 by Google Books for keyword mathematics about sets.
Book ID of Higher Topos Theory (AM-170)'s Books is gP2MtT99g7MC, Book which was written byJacob Luriehave ETAG "NFstanE/jNY"
Book which was published by Princeton University Press since 2009-07-06 have ISBNs, ISBN 13 Code is 9781400830558 and ISBN 10 Code is 1400830559
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