论文标题
$ \ infty $ - 类别本地化函数，用于简单集的图表
An $\infty$-categorical localisation functor for diagrams of simplicial sets
论文作者
论文摘要
与每个小型类别$ c $相关联，有一个类别的$ c $形式的简单套装图和$ \ infty $ - 类别的$ nc $ - 形状 - 形状的同型相干图。我们提出了一个函子，后者是前者在对象方弱同质均值等效上的$ \ infty $分类定位。这是建立在与Heuts-Moerdijk有关的$ c $相关的投影和协变量模型结构之间的基础上，以及Cisinski的$ \ infty $分类本地化理论。我们使用本地化函数提供简化的证据，证明左侧（右）同质kan kan simplicial集的图表显示了$ \ infty $ - infty $ - 分类左（分别为右）kan kan kan sepension of Spaces相干图的扩展。
Associated to each small category $C$, there is a category of $C$-shaped diagrams of simplicial sets and an $\infty$-category of $NC$-shaped homotopy coherent diagrams of spaces. We present a functor which exhibits the latter as the $\infty$-categorical localisation of the former at the objectwise weak homotopy equivalences. This builds on a Quillen equivalence between the projective and covariant model structures associated to $C$ due to Heuts-Moerdijk, as well as Cisinski's theory of $\infty$-categorical localisations. We use the localisation functor to give simplified proofs that the left (resp. right) homotopy Kan extension of diagrams of simplicial sets presents the $\infty$-categorical left (resp. right) Kan extension of coherent diagrams of spaces.
