A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen
Abstract
Description
We define a closed model category containing the $n$-nerves defined by Tamsamani, and admitting internal $Hom$. This allows us to construct the $n+1$-category $nCAT$ by taking the internal $Hom$ for fibrant objects. We prove a generalized Seifert-Van Kampen theorem for Tamsamani's Poincaré $n$-groupoid of a topological space. We give a still-speculative discussion of $n$-stacks, and similarly of comparison with other possible definitions of $n$-category.
Corrects an error in the proof of Theorem 5.1, by rewriting locally. Doesn't change the rest of the text, so numerous expositional problems are left untouched
Corrects an error in the proof of Theorem 5.1, by rewriting locally. Doesn't change the rest of the text, so numerous expositional problems are left untouched