Title: Groupoidal and truncated $n$-quasi-categories Show Chinese title

Title: 群oidal 和截断的$n$-准范畴

Abstract: We define groupoidal and $(n+k)$-truncated $n$-quasi-categories, which are the translation to the world of $n$-quasi-categories of groupoidal and truncated $(\infty, n)$-$\Theta$-spaces defined by Rezk. We show that these objects are the fibrant objects of model structures on the category of presheaves on $\Theta_n$ obtained by localisation of Ara's model structure for $n$-quasi-categories. Furthermore, we prove that the inclusion $\Delta \to \Theta_n$ induces a Quillen equivalence between the model structure for groupoidal (resp. and $n$-truncated) $n$-quasi-categories and the Kan-Quillen model structure for spaces (resp. homotopy $n$-types) on simplicial sets. To get to these results, we also construct a cylinder object for $n$-quasi-categories. Show Chinese abstract

Abstract: 我们定义了群素的和$(n+k)$-截断的$n$-准范畴，这些是将 Rezk 定义的群素和截断的$(\infty, n)$-$\Theta$-空间翻译到$n$-准范畴世界中的结果。 我们证明这些对象是通过局部化 Ara 对$n$-准范畴的模型结构，在预层范畴$\Theta_n$上得到的模型结构中的纤维对象。 此外，我们证明包含关系$\Delta \to \Theta_n$在群域（相应地，和$n$-截断）$n$-准范畴的模型结构与单纯集上的空间（相应地，同伦$n$-类型）的Kan-Quillen模型结构之间诱导了一个Quillen等价。为了得到这些结果，我们还为$n$-准范畴构造了一个圆柱对象。