Corollary 9.4.8.6 (Accessibility of Slices). Let $\operatorname{\mathcal{C}}$ be an accessible $\infty $-category and let $F: K \rightarrow \operatorname{\mathcal{C}}$ be a small diagram. Then the slice and coslice $\infty $-categories $\operatorname{\mathcal{C}}_{/F}$ and $\operatorname{\mathcal{C}}_{F/}$ are accessible.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Combine Propositions 9.4.8.1 and 9.4.8.4 with the equivalences
\[ \operatorname{\mathcal{C}}_{/F} \hookrightarrow \operatorname{\mathcal{C}}\vec{\times }_{ \operatorname{Fun}(K, \operatorname{\mathcal{C}}) } \{ F \} \quad \quad \operatorname{\mathcal{C}}_{F/} \hookrightarrow \{ F\} \vec{\times }_{ \operatorname{Fun}(K, \operatorname{\mathcal{C}}) } \operatorname{\mathcal{C}} \]
supplied by Theorem 4.6.4.19. $\square$