# Kerodon

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Example 4.6.1.6. Let $\operatorname{\mathcal{C}}$ be a simplicial set containing vertices $X$ and $Y$. Let $K$ be a simplicial set, and let $\underline{X}, \underline{Y}: K \rightarrow \operatorname{\mathcal{C}}$ be the constant maps taking the values $X$ and $Y$, respectively. Then there is a canonical isomorphism of simplicial sets

$\operatorname{Hom}_{ \operatorname{Fun}(K, \operatorname{\mathcal{C}}) }( \underline{X}, \underline{Y} ) \simeq \operatorname{Fun}(K, \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y) ).$