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