论文标题
DWYER地图的推翻为$（\ infty，1）$ - 分类
Pushouts of Dwyer maps are $(\infty,1)$-categorical
论文作者
论文摘要
将1类纳入$（\ infty，1）$ - 类别通常无法保留colimits，尤其是下拉菜。在本说明中，我们观察到，如果一个类别中的一个函子属于某些先前识别的函子类，则在此包含下将保留1类分类的求职者。 Dwyer Maps是一种类别的邻域变形缩回，Thomason在其1类中的模型结构的构建中使用了。托马森（Thomason）先前观察到，此类定位的神经具有正确的弱同质型。我们完善了这一结果，并表明弱的同位等效性是一个弱分类等效性。我们还确定了一个更通用的函子，其中1类分类的下降菜是$（\ infty，1）$ - 分类。
The inclusion of 1-categories into $(\infty,1)$-categories fails to preserve colimits in general, and pushouts in particular. In this note, we observe that if one functor in a span of categories belongs to a certain previously-identified class of functors, then the 1-categorical pushout is preserved under this inclusion. Dwyer maps, a kind of neighborhood deformation retract of categories, were used by Thomason in the construction of his model structure on 1-categories. Thomason previously observed that the nerves of such pushouts have the correct weak homotopy type. We refine this result and show that the weak homotopical equivalence is a weak categorical equivalence. We also identify a more general class of functors along which 1-categorical pushouts are $(\infty,1)$-categorical.
