Remark 5.4.6.10. 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 four-out-of-five-property, then the inverse image $F^{-1}(T)$ also has the four-out-of-five property.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$