论文标题
群体素作为同型类型的模型
Presheaves of groupoids as models for homotopy types
论文作者
论文摘要
我们介绍了群体（弱）测试类别的概念，该类别是一个小类别A，因此以“规范且不错的方式”的方式对同型同副本类型的模型类型进行了类型的预选。该定义不需要先验A是（弱）测试类别，但是我们证明了Twon重要的比较结果：（1）每个弱测试类别是一个群体弱测试类别，（2）一个类别是测试类别，并且仅当它是群体测试类别时。作为应用程序，我们获得了同型类型的新模型，例如内部与有或没有连接的立方组的类别类别，类别的类别类别是细胞集的内部，类别的类别类别的类别类别的类别对半震动的组合等。我们还可以预见，作为副产品的结果，类别是小型类型的小型类型。
We introduce the notion of groupoidal (weak) test category, which is a small category A such that the groupoid-valued presheaves over A models homotopy types in a "canonical and nice" way. The definition does not require a priori that A is a (weak) test category, but we prove twon important comparison results: (1) every weak test category is a groupoidal weak test category, (2) a category is a test category if and only if it is a groupoidal test category. As an application, we obtain new models for homotopy types, such as the category of groupoids internal to cubical sets with or without connections, the category of groupoids internal to cellular sets, the category of groupoids internal to semi-simplicial sets, etc. We also prove, as a by-product result, that the category of groupoids internal to the category of small categories models homotopy types.
