论文标题
更高对应的简单类别
A simplicial category for higher correspondences
论文作者
论文摘要
在这项工作中，我们提出了卢里（Lurie）预测的意识，即内部纤维$ p：x \ rightarrow a $由$ a $ a $ index的图表归类为``高等类别''的对象，其对象为$ \ infty $ \ infty $ - 类别，形态性是它们之间的相互作用和较高的相互作用的相互作用，我们将获得更多的阶段。简单套装以类似的方式。 简单集（和$ \ infty $ - 类别）之间的对应关系是与类别有关的分解器（或bimodule）概念的概括。虽然类别，函子和分配器是在双重类别中组织的，但我们将作为简单类别的一部分展示简单集，简单地图和对应关系。这使我们能够做出精确的陈述并提供证据。我们的主要工具是双重类别的语言，我们在简单类别的上下文中也使用。
In this work we propose a realization of Lurie's prediction that inner fibrations $p: X \rightarrow A$ are classified by $A$-indexed diagrams in a ``higher category" whose objects are $\infty$-categories, morphisms are correspondences between them and higher morphisms are higher correspondences. We will obtain this as a corollary of a more general result which classifies all simplicial maps between ordinary simplicial sets in a similar fashion. Correspondences between simplicial sets (and $\infty$-categories) are a generalization of the concept of profunctor (or bimodule) pertaining to categories. While categories, functors and profunctors are organized in a double category, we will exhibit simplicial sets, simplicial maps, and correspondences as part of a simplicial category. This allows us to make precise statements and provide proofs. Our main tool is the language of double categories, which we use in the context of simplicial categories as well.
