Kerodon

Corollary 7.1.6.12. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $B$ be a simplicial set, and let $\overline{f}: K^{\triangleright } \rightarrow \operatorname{Fun}(B,\operatorname{\mathcal{C}})$ be a diagram. Assume that, for each vertex $b \in B$, the composite map $K^{\triangleright } \xrightarrow { \overline{f} } \operatorname{Fun}(B,\operatorname{\mathcal{C}}) \xrightarrow { \operatorname{ev}_ b } \operatorname{\mathcal{C}}$ is a colimit diagram in $\operatorname{\mathcal{C}}$. Then $\overline{f}$ is a colimit diagram in $\operatorname{Fun}(B,\operatorname{\mathcal{C}})$.