# Kerodon

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

Remark 4.6.7.13. Let $K$ be a simplicial set, and let $\operatorname{\mathcal{D}}$ be another simplicial set containing vertices $X$ and $Y$. Unwinding the definitions, we have a canonical bijection

$\xymatrix@R =50pt@C=50pt{ \{ \textnormal{Morphisms K \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{D}}}^{\mathrm{L}}(X,Y)} \} \ar [d]^{\sim } \\ \{ \textnormal{Morphisms F: \Sigma (K) \rightarrow \operatorname{\mathcal{D}} with F(x) = X and F(y) = Y} \} . }$