Title: Cartesian Fibrations of Complete Segal Spaces Show Chinese title

Title: 笛卡尔纤维化完全塞加空间

Abstract: Cartesian fibrations were originally defined by Lurie in the context of quasi-categories and are commonly used in $(\infty,1)$-category theory to study presheaves valued in $(\infty,1)$-categories. In this work we define and study fibrations modeling presheaves valued in simplicial spaces and their localizations. This includes defining a model structure for these fibrations and giving effective tools to recognize its fibrations and weak equivalences. This in particular gives us a new method to construct Cartesian fibrations via complete Segal spaces. In addition to that, it allows us to define and study fibrations modeling presheaves of Segal spaces. Show Chinese abstract

Abstract: 笛卡尔纤维最初由Lurie在准范畴的背景下定义，并常用于$(\infty,1)$-范畴论中研究取值于$(\infty,1)$-范畴的预层。 在本工作中，我们定义并研究模拟取值于单纯空间及其局部化的预层的纤维。 这包括为这些纤维定义一个模型结构，并提供有效的工具来识别其纤维和弱等价。 这特别使我们能够通过完整Segal空间构建新的笛卡尔纤维方法。 此外，它还允许我们定义并研究模拟Segal空间预层的纤维。