Warning 5.4.6.9. Definition 5.4.6.8 is not self-dual. Let $T$ be a collection of $2$-simplices of $\operatorname{\mathcal{C}}$ which satisfies the four-out-of-five property and let $T^{\operatorname{op}}$ denote the same set, regarded as a collection of $2$-simplices of the opposite simplicial set $\operatorname{\mathcal{C}}^{\operatorname{op}}$. Then $T^{\operatorname{op}}$ need not satisfy the four-out-of-five property.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$