A Quillen model structure for Gray-categories
Category Theory
2011-10-19 v2 Algebraic Topology
Abstract
A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full subcategory Gray-Gpd of Gray-groupoids. This is used to provide a functorial and model-theoretic proof of the unpublished theorem of Joyal and Tierney that Gray-groupoids model homotopy 3-types. The model structure on Gray-Cat is conjectured to be Quillen equivalent to a model structure on the category Tricat of tricategories and strict homomorphisms of tricategories.
Cite
@article{arxiv.1001.2366,
title = {A Quillen model structure for Gray-categories},
author = {Stephen Lack},
journal= {arXiv preprint arXiv:1001.2366},
year = {2011}
}
Comments
v2: fuller discussion of relationship with work of Berger; localizations are done directly with simplicial sets