Kerodon

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

Corollary 8.5.1.13. Let $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be an inner fibration of $\infty $-categories and let $f$ be a $U$-cocartesian morphism in $\operatorname{\mathcal{D}}$. Then any retract of $f$ (in the $\infty $-category $\operatorname{Fun}(\Delta ^1, \operatorname{\mathcal{C}})$) is also $U$-cocartesian.

Proof. Apply Corollary 8.5.1.11 in the special case $K = \Delta ^0$ (see Example 7.1.6.9). $\square$