论文标题
$（\ infty，n）$类别的同型连贯神经
A homotopy coherent nerve for $(\infty,n)$-categories
论文作者
论文摘要
在$（\ infty，1）$ - 类别的情况下，同型连贯的神经在简单丰富类别和准类别的模型之间具有正确的quillen等效性。这表明，$（\ infty，1）$ - 类别的同质副本相干图可以等效地定义为准类别的函数，或者是从同型相干分类中简单地富集的函数。 在本文中，我们以$（\ infty，n）$类别构建了同型连贯的神经。我们表明，它在$（\ infty，n-1）$ - 类别中严格丰富的类别模型之间实现了正确的quillen等价性，而Segal类别对象则以$（\ infty，n-1）$ - 类别为单位。同样，这使我们能够将$（\ infty，n）$ - 类别定义为segal类别对象的函数或从同型相干分类中的严格富集函数等效地等同。
In the case of $(\infty,1)$-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories. This shows that homotopy coherent diagrams of $(\infty,1)$-categories can equivalently be defined as functors of quasi-categories or as simplicially enriched functors out of the homotopy coherent categorifications. In this paper, we construct a homotopy coherent nerve for $(\infty,n)$-categories. We show that it realizes a right Quillen equivalence between the models of categories strictly enriched in $(\infty,n-1)$-categories and of Segal category objects in $(\infty,n-1)$-categories. This similarly enables us to define homotopy coherent diagrams of $(\infty,n)$-categories equivalently as functors of Segal category objects or as strictly enriched functors out of the homotopy coherent categorifications.
