Kerodon

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

Remark 4.6.1.7. Let $\operatorname{\mathcal{C}}$ be a simplicial set containing vertices $X$ and $Y$, which we also regard as vertices of the opposite simplicial set $\operatorname{\mathcal{C}}^{\operatorname{op}}$. Then there is a canonical isomorphism of simplicial sets $\operatorname{Hom}_{\operatorname{\mathcal{C}}^{\operatorname{op}} }( X, Y) \simeq \operatorname{Hom}_{\operatorname{\mathcal{C}}}(Y,X)^{\operatorname{op}}$.