Quasi-categories and Kan complexes

被引：167

作者：

Joyal, A ^{[1
]}

机构：

[1] Univ Quebec, Dept Math, Montreal, PQ H3C 3P8, Canada

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2002年 / 175卷 / 1-3期

关键词：

D O I：

10.1016/S0022-4049(02)00135-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A quasi-category X is a simplicial set satisfying the restricted Kan conditions of Boardman and Vogt. It has an associated homotopy category hoX. We show that X is a Kan complex iff hoX is a groupoid. The result plays an important role in the theory of quasi-categories (in preparation). Here we make an application to the theory of initial objects in quasi-categories. We briefly discuss the notions of limits and colimits in quasi-categories. (C) 2002 Published by Elsevier Science B.V.

引用

页码：207 / 222

页数：16

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