Corollary 10.2.5.22. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories, let $C_{\bullet }$ be an augmented (semi)simplicial object of $\operatorname{\mathcal{C}}$, and let $n \geq -1$ be an integer. Assume that $\operatorname{\mathcal{C}}$ admits pullbacks and that $F$ preserves pullbacks. If $C_{\bullet }$ is $n$-coskeletal, then the image $F( C_{\bullet } )$ is $n$-coskeletal.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$