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arXiv · 2412.15715

Double categorical model of $(\infty,1)$-categories

Léonard Guetta·Lyne Moser
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Abstract

Building on work by Fiore-Pronk-Paoli, we construct four model structures on the category of double categories, each modeling one of the following: simplicial spaces, Segal spaces, $(\infty,1)$-categories, and $\infty$-groupoids. Additionally, we provide an explicit formula for computing homotopy colimits in these models using the Grothendieck construction. We expect the model of double categories for $(\infty,1)$-categories to play a similar role than that of the model of categories for spaces or $\infty$-groupoids in Grothendieck's study of the homotopy theory of spaces.

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Léonard Guetta, Lyne Moser. 2024-12-20. Double categorical model of $(\infty,1)$-categories. https://arxiv.org/abs/2412.15715

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