Variant 7.1.3.10. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a fully faithful functor of $\infty $-categories and let $\overline{u}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$ be a morphism of simplicial sets. If $F \circ \overline{u}$ is a limit diagram in the $\infty $-category $\operatorname{\mathcal{D}}$, then $\overline{u}$ is a limit diagram in the $\infty $-category $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$