Remark 5.4.5.9. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets and let $T$ be a collection of $2$-simplices of $\operatorname{\mathcal{D}}$. If $T$ has the inner exchange property, then the inverse image $F^{-1}(T)$ has the inner exchange property.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$