Definition 7.1.8.13. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories and let $K$ and $B$ be simplicial sets. We say that a diagram $\overline{f}: K^{\triangleright } \rightarrow \operatorname{Fun}(B,\operatorname{\mathcal{C}})$ is a levelwise $F$-colimit diagram if, for each vertex $b \in B$, the composition $(\operatorname{ev}_{b} \circ \overline{f}): K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is an $F$-colimit diagram in the $\infty $-category $\operatorname{\mathcal{C}}$.
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