论文标题
$ n $ - 分类神经的比较
Comparison of the $n$-categorical nerves
论文作者
论文摘要
我们的目的是将三个神经函子用于严格的$ n $分类：街道神经，细胞神经和多动神经。我们表明，这三个函子在某种意义上是等效的。特别是，它们定义的$ n $分类弱等价类别的类别是thomason等价。我们给出了这两个结果的两种应用：第一个指出，托马森等价的染料 - 智型等效性是托马森对等。第二个是基本的，是在严格的$ n $类别类别的二重性下，托马森等价类别的稳定性。
Our aim is to compare three nerve functors for strict $n$-categories: the Street nerve, the cellular nerve and the multi-simplicial nerve. We show that these three functors are equivalent in some appropriate sense. In particular, the classes of $n$-categorical weak equivalences that they define coincide: they are the Thomason equivalences. We give two applications of this result: the first one states that a Dyer-Kan-type equivalence for Thomason equivalences is a Thomason equivalence; the second one, fundamental, is the stability of the class of Thomason equivalences under the dualities of the category of strict $n$-categories.
