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Exercise Let $f: X \rightarrow S$ be an inner covering map of simplicial sets and let $i: A \hookrightarrow B$ be any monomorphism of simplicial sets. Show that the restriction map

\[ \theta : \operatorname{Fun}( B_{}, X_{} ) \rightarrow \operatorname{Fun}( B_{}, S_{} ) \times _{ \operatorname{Fun}( A_{}, S_{} )} \operatorname{Fun}( A_{}, X_{} ) \]

is also an inner covering map. If $i$ is inner anodyne, show that $\theta $ is an isomorphism.