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arXiv · 1905.05625

On the homotopy hypothesis in dimension 3

Simon Henry·Edoardo Lanari
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Abstract

We show that if the canonical left semi-model structure on the category of Grothendieck $n$-groupoids exists, then it satisfies the homotopy hypothesis, i.e. the associated $(\infty,1)$-category is equivalent to that of homotopy $n$-types, thus generalizing a result of the first named author. As a corollary of the second named author's proof of the existence of the canonical left semi-model structure for Grothendieck 3-groupoids, we obtain a proof of the homotopy hypothesis for Grothendieck 3-groupoids.

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Simon Henry, Edoardo Lanari. 2019-05-14. On the homotopy hypothesis in dimension 3. https://arxiv.org/abs/1905.05625

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