Kerodon

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

Corollary 5.3.3.4. Let $\operatorname{\mathcal{C}}$ be an $(\infty ,2)$-category and let $f: K \rightarrow \operatorname{\mathcal{C}}$ be a morphism of simplicial sets. Then the simplicial sets $\operatorname{\mathcal{C}}_{f/}$ and $\operatorname{\mathcal{C}}_{/f}$ are $(\infty ,2)$-categories.

Proof. Combine Proposition 5.3.3.1 with Proposition 5.3.2.8. $\square$