Grothendieck's Homotopy Hypothesis
Algebraic Topology
2011-12-07 v1 Category Theory
K-Theory and Homology
Abstract
We construct a "diagonal" cofibrantly generated model structre on the category of simplicial objects in the category of topological categories sCat_{Top}, which is the category of diagrams [\Delta^{op}, Cat_{Top}]. Moreover, we prove that the diagonal model structures is left proper and cellular. We also prove that the category of \infty-groupoids (the full subcategory of topological categories) has a cofibrantly generated model structure and is Quillen equivalent to the model category of simplicial sets, which proves the Grothendieck's homotopy hypothesis.
Cite
@article{arxiv.1112.1251,
title = {Grothendieck's Homotopy Hypothesis},
author = {Ilias Amrani},
journal= {arXiv preprint arXiv:1112.1251},
year = {2011}
}