标题： $(\infty,1)$-范畴的双重范畴模型 显示英文标题

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

摘要： 在Fiore-Pronk-Paoli工作的基础上，我们在双范畴的范畴上构建了四种模型结构，每种模型分别对应以下内容：单纯空间、Segal空间、$(\infty,1)$-范畴和$\infty$-群胚。 此外，我们提供了一个显式公式，用于在这些模型中计算同伦余极限，使用的是Grothendieck构造。 我们预计双范畴对$(\infty,1)$-范畴的模型将在Grothendieck对空间同伦理论的研究中起到与范畴对空间或$\infty$-群胚模型相似的作用。 显示英文摘要

摘要： 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.