2024/12/20 by Léonard Guetta, Guetta, Léonard, Lyne Moser +1
Computer Science · #Rough Sets and Fuzzy Logic #Image Retrieval and Classification Techniques
paper · pdf · doi:10.48550/arxiv.2412.15715
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, (∞,1)-categories, and ∞-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 (∞,1)-categories to play a similar role than that of the model of categories for spaces or ∞-groupoids in Grothendieck's study of the homotopy theory of spaces.