# Kerodon

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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 $\operatorname{Hom}_{\operatorname{\mathcal{C}}^{\operatorname{op}} }( X, Y) \simeq \operatorname{Hom}_{\operatorname{\mathcal{C}}}(Y,X)^{\operatorname{op}}$.