Kerodon

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

Corollary 8.5.1.11. Let $K$ be a simplicial set and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories which preserves $K$-indexed colimits. If $G: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is a retract of $F$ (in the $\infty $-category $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$), then $G$ also preserves $K$-indexed colimits.