Corollary 7.1.7.8. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an inner fibration of $\infty $–categories, let $C \in \operatorname{\mathcal{C}}$ be an object, and let
\[ \overline{q}: K^{\triangleright } \rightarrow \operatorname{\mathcal{E}}_{C} = \{ C\} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}} \]
be a diagram. If $\overline{q}$ is a $U$-colimit diagram in the $\infty $-category $\operatorname{\mathcal{E}}$, then it is a colimit diagram in the $\infty $-category $\operatorname{\mathcal{E}}_{C}$.