Weak complicial sets I. Basic homotopy theory
Weak complicial sets I. Basic homotopy theory
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弱共合集 I. 基本同伦理论
DOI：
10.1016/j.aim.2008.06.003
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发表时间：
2008
影响因子：
1.7
通讯作者：
Dominic R. Verity
中科院分区：
文献类型：
--
作者：
Dominic R. Verity
本文发展了弱ω-范畴的单形理论的基础，它建立在Ross Street在1987年关于定向单形的论文中最初阐述的见解之上。由此产生的弱复集理论提供了（严格）ω-范畴、Kan复体和Joyal准范畴理论的共同概括。我们概括了一些结果，由于目前的作者关于复杂集和严格的ω-范畴，提供了一个军械库的良好表现的技术设备，如连接和灰色张量积，这将被用来研究弱ω-范畴理论的这些结构在一系列的配套文件。特别地，我们通过构造以弱复集为映射对象的层单纯集范畴上的Quillen模型结构，建立了它们的基本同伦理论。作为一个简单的推论，这项工作，我们提供了一个独立的建设Joyal的模型结构的单纯集的准范畴的对象。
This paper develops the foundations of a simplicial theory of weak ω-categories, which builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented simplices. The resulting theory of weak complicial sets provides a common generalisation of the theories of (strict) ω-categories, Kan complexes and Joyal's quasi-categories. We generalise a number of results due to the current author with regard to complicial sets and strict ω-categories to provide an armoury of well behaved technical devices, such as joins and Gray tensor products, which will be used to study the weak ω-category theory of these structures in a series of companion papers. In particular, we establish their basic homotopy theory by constructing a Quillen model structure on the category of stratified simplicial sets whose fibrant objects are the weak complicial sets. As a simple corollary of this work we provide an independent construction of Joyal's model structure on simplicial sets for which the fibrant objects are the quasi-categories.