Kerodon

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

Remark 5.3.5.8. Let $\operatorname{\mathcal{C}}$ be a simplicial set, let $T$ be a collection of $2$-simplices of $\operatorname{\mathcal{C}}$, and let $T^{\operatorname{op}}$ denote the set $T$, regarded as a collection of simplices of the opposite simplicial set $\operatorname{\mathcal{C}}^{\operatorname{op}}$. Then $T$ has the inner exchange property if and only if $T^{\operatorname{op}}$ has the inner exchange property.