论文标题
拓扑类别类别的均匀类型
Homotopy types of topological stacks of categories
论文作者
论文摘要
本说明将Quillen的定理A扩展到拓扑空间内部的大型类别。这使我们能够证明，在温和的情况下，在此类拓扑类别之间完全忠实且本质上是溢出的函子会引起分类空间的同等相等。得出的结论是，我们可以将2个功能的同质类型与类别的一系列拓扑堆栈相关联，在2类空间，连续地图和地图同质的同型类别中取值。这将Noohi和Ebert在限制到该站点的拓扑堆栈的同质类型的类型上进行了概括。
This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essentially surjective functor between such topological categories induces a homotopy equivalence of classifying spaces. It follows from this that we can associate a 2-functorial homotopy type to a wide class of topological stacks of categories, taking values in the 2-category of spaces, continuous maps and homotopy classes of homotopies of maps. This generalises work of Noohi and Ebert on the homotopy types of topological stacks of groupoids under the restriction to the site with numerable open covers.
