# Kerodon

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

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.