Remark 11.5.0.118. Let $S$ be a simplicial set, and let $(\operatorname{Set_{\Delta }})_{/S}$ denote the slice category of simplicial sets $X$ equipped with a morphism $q_{X}: X \rightarrow S$. Then we can regard $(\operatorname{Set_{\Delta }})_{/S}$ as a simplicially enriched category, with mapping simplicial sets given by
\[ \underline{\operatorname{Hom}}_{ ( \operatorname{Set_{\Delta }})_{/S} }( X, Y) = \operatorname{Fun}_{S}(X,Y). \]