Proposition 9.5.4.17. Let $\operatorname{\mathcal{C}}$ be a small simplicial set and let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a presentable fibration. Then the $\infty $-category of sections $\operatorname{Fun}_{ / \operatorname{\mathcal{C}}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{E}})$ is presentable. Moreover, for each vertex $C \in \operatorname{\mathcal{C}}$, the evaluation functor $\operatorname{Fun}_{ / \operatorname{\mathcal{C}}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{E}}) \rightarrow \operatorname{Fun}_{ / \operatorname{\mathcal{C}}}( \{ C\} , \operatorname{\mathcal{E}}) = \operatorname{\mathcal{E}}_{C}$ preserves small limits and colimits.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof of Proposition 9.5.4.17. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a presentable fibration of simplicial sets. It follows from Proposition 9.5.3.7 that $U$ is an edgewise accessible inner fibration which is both locally cartesian and locally cocartesian. The desired result now follows by combining Lemma 9.5.4.19 with Remark 9.5.4.20. $\square$