# Kerodon

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Lemma 4.6.7.16. Let $K$ be a simplicial set and let $\operatorname{\mathcal{C}}$ be a simplicial category containing objects $X$ and $Y$. Then the natural map

$\xymatrix@R =50pt@C=50pt{ \{ \textnormal{Functors F: \operatorname{Path}[\Sigma (K)]_{\bullet } \rightarrow \operatorname{\mathcal{C}} with F(x) = X and F(y) = Y} \} \ar [d] \\ \{ \textnormal{Morphisms \Phi (K) \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{\bullet }} \} }$

is a bijection.