A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen

Details A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen

1997-04-10

arxiv.org/abs/alg-geom/9704006v2

Mathematics

Algebraic Geometry

Corrects an error in the proof of Theorem 5.1, by rewriting locally. Doesn't change the rest of the text, so numerous expositi

Scientific paper

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 Poincar\'e $n$-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.

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