Warning 5.1.7.11. The conclusion of Proposition 5.1.7.10 does not necessarily hold if $V: \widetilde{\operatorname{\mathcal{D}}} \rightarrow \operatorname{\mathcal{D}}$ is assumed only to be an inner fibration of simplicial sets. See Warning 5.1.7.6.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$