Corollary 7.3.8.8. Let $K$ be a simplicial set and let $\operatorname{\mathcal{D}}$ be an $\infty $-category. Then the collection of colimit diagrams $K^{\triangleright } \rightarrow \operatorname{\mathcal{D}}$ is closed under the formation of levelwise colimits (in the $\infty $-category $\operatorname{Fun}( K^{\triangleright }, \operatorname{\mathcal{D}})$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 7.3.8.6 in the special case $\operatorname{\mathcal{E}}= \Delta ^0$. $\square$