Grothendieck's Homotopy Hypothesis

Details Grothendieck's Homotopy Hypothesis Grothendieck's Homotopy Hypothesis

2011-12-06

arxiv.org/abs/1112.1251v1

Mathematics

Algebraic Topology

Scientific paper

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.

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