Remark 3.1.3.9. Suppose we are given a diagram of simplicial sets
\[ \xymatrix@R =50pt@C=50pt{ A \ar [r]^-{f} \ar [d]^{i} & X \ar [d]^{q} \\ B \ar [r]^-{g} \ar@ {-->}[ur]^{ \overline{f} } & S } \]
which does not commute. Then the simplicial set $\operatorname{Fun}_{A/ \, /S}(B,X) = \operatorname{Fun}_{A/}(B,X) \cap \operatorname{Fun}_{/S}(B,X)$ of Construction 3.1.3.7 can still be defined, but is automatically empty.