论文标题
$（\ infty，1）$ - 类别的立方模型
Cubical models of $(\infty, 1)$-categories
论文作者
论文摘要
我们在立方组的类别上构建了一个模型结构，其连接的联合启动是单态性，其纤维对象是由右抬起特性相对于内部敞开的盒子（内角的立方类似物）来定义的。我们表明，这种模型结构是通过三角仪函子在简单集上的Joyal模型结构等同的quillen。作为一种应用，我们表明立方准游戏允许绘制空间的方便概念，我们用来将模型结构中的纤维对象之间的弱等价表征为DK等效性。
We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We show that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor. As an application, we show that cubical quasicategories admit a convenient notion of a mapping space, which we use to characterize the weak equivalences between fibrant objects in our model structure as DK-equivalences.
