Corollary 7.1.7.15. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a locally cartesian fibration of $\infty $-categories, let $C \in \operatorname{\mathcal{C}}$ be an object, and let $\overline{q}: K^{\triangleright } \rightarrow \operatorname{\mathcal{E}}_{C}$ be a morphism of simplicial sets. Then $\overline{q}$ is a $U$-colimit diagram in the $\infty $-category $\operatorname{\mathcal{E}}$ if and only if it is a colimit diagram in the $\infty $-category $\operatorname{\mathcal{E}}_{C}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$