Kerodon

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

Corollary 8.5.1.12. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category and let $f,g: K^{\triangleright } \rightarrow \operatorname{\mathcal{D}}$ be diagrams. If $f$ is a colimit diagram and $g$ is a retract of $f$, then $g$ is also a colimit diagram.

Proof. Apply Corollary 8.5.1.11 in the special case $\operatorname{\mathcal{E}}= \Delta ^0$. $\square$