Remark 11.10.6.7. Let $q: Y \rightarrow S$ be a morphism of simplicial sets. Then the construction $X \mapsto \operatorname{Fun}_{/S}(X,Y)$ carries colimits in the slice category $( \operatorname{Set_{\Delta }})_{/S}$ to limits in the category of simplicial sets. In particular, $\operatorname{Fun}_{/S}( \emptyset , Y)$ can be identified with the $0$-simplex $\Delta ^{0}$.
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