Corollary 9.4.6.16. A functor of $\infty $-categories $U: \operatorname{\mathcal{E}}\rightarrow \Delta ^2$ is a flat inner fibration if and only if the inclusion map $\Lambda ^{2}_{1} \times _{\Delta ^2} \operatorname{\mathcal{E}}\hookrightarrow \operatorname{\mathcal{E}}$ is a categorical equivalence of simplicial sets.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$