Corollary 4.2.3.2. Let $f: X_{} \rightarrow S_{}$ be a morphism of simplicial sets, let $B_{}$ be an arbitrary simplicial set, and let $\rho : \operatorname{Fun}( B_{}, X_{} ) \rightarrow \operatorname{Fun}( B_{}, S_{} )$ be the morphism induced by composition with $f$. If $f$ is a left fibration, then $\rho $ is a left fibration. If $f$ is a right fibration, then $\rho $ is a right fibration.

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