Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 7.1.7.15. 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 levelwise colimit diagram. Then $\overline{f}$ is a colimit diagram in $\operatorname{Fun}(B,\operatorname{\mathcal{C}})$.

Proof. Apply Corollary 7.1.7.14 in the special case $\operatorname{\mathcal{D}}= \Delta ^0$ (or Corollary 7.1.7.13) in the special case $A = \emptyset $. $\square$