Grothendieck's Homotopy Hypothesis

Ilias Amrani

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arXiv · 1112.1251

Grothendieck's Homotopy Hypothesis

Ilias Amrani

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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.

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BibTeX RIS

Ilias Amrani. 2011-12-06. Grothendieck's Homotopy Hypothesis. https://arxiv.org/abs/1112.1251

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