Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Proposition 5.5.5.2. The simplicial set $\operatorname{ \pmb {\mathcal{QC}} }$ is an $(\infty ,2)$-category.

Proof. For every pair of $\infty $-categories $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$, Theorem 1.4.3.7 guarantees that the simplicial set $\operatorname{Hom}_{\operatorname{\mathbf{QCat}}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})_{\bullet } = \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ is an $\infty $-category. The desired result is now a special case of Theorem 5.4.8.1. $\square$