Corollary 7.1.9.5. Let $F_0: \operatorname{\mathcal{C}}_0 \rightarrow \operatorname{\mathcal{C}}$ and $F_1: \operatorname{\mathcal{C}}_1 \rightarrow \operatorname{\mathcal{C}}$ be functors of $\infty $-categories and let $K$ be a simplicial set satisfying the following conditions:
The $\infty $-category $\operatorname{\mathcal{C}}_0$ admits $K$-indexed colimits, which are preserved by the functor $F_0$.
The $\infty $-category $\operatorname{\mathcal{C}}_1$ admits $K$-indexed colimits.
Then the oriented fiber product $\operatorname{\mathcal{C}}_0 \vec{\times }_{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_1$ also admits $K$-indexed colimits. Moreover, a morphism of simplicial sets $\overline{q}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}_0 \vec{\times }_{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_1$ is a colimit diagram if and only if its images in $\operatorname{\mathcal{C}}_0$ and $\operatorname{\mathcal{C}}_1$ are colimit diagrams.