Higher Topos Theory

出版者:Princeton University Press

作者:Jacob Lurie

页数:944

出版时间:2009-7-26

价格:USD 75.00

装帧:Paperback

isbn号码:9780691140490

丛书系列:Annals of Mathematics Studies

图书标签:数学category范畴学higherMathematics高维范畴论想买topology

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.

用户评价

读了前五章，其实没涉及到最重要的∞-topoi. 一开始以为会很难而且枯燥，后来发现根本没这回事——这是一门很有意思的语言，只是需要些耐心罢了。如果预先熟悉过∞-categories的语言，基本上是没有理解上的障碍的。我觉得Charles Rezk的course notes "stuff about quasicategories" 很不错。

读了前五章，其实没涉及到最重要的∞-topoi. 一开始以为会很难而且枯燥，后来发现根本没这回事——这是一门很有意思的语言，只是需要些耐心罢了。如果预先熟悉过∞-categories的语言，基本上是没有理解上的障碍的。我觉得Charles Rezk的course notes "stuff about quasicategories" 很不错。

概念太多，感觉读一遍还是不能很好的把握

读了前五章，其实没涉及到最重要的∞-topoi. 一开始以为会很难而且枯燥，后来发现根本没这回事——这是一门很有意思的语言，只是需要些耐心罢了。如果预先熟悉过∞-categories的语言，基本上是没有理解上的障碍的。我觉得Charles Rezk的course notes "stuff about quasicategories" 很不错。

概念太多，感觉读一遍还是不能很好的把握