Grothendieck's Homotopy Hypothesis

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 [Δ^{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.

References in corpus (1)

• A Model Structure on the Category of Topological Categories

Cited by in corpus (3)

• Moduli space of fibrations in the category of simplicial presheaves
• Stabilization of the category of simplicial objects in CAT
• The Friedlander-Milnor conjectures