Corollary 4.3.6.9. Let $q: X \rightarrow S$ be an inner fibration of simplicial sets and let $f: K \rightarrow X$ be any morphism of simplicial sets. Then the restriction map
\[ X_{/f} \rightarrow X \times _{S} S_{ / (q \circ f)} \]
is a right fibration, and the restriction map
\[ X_{f/} \rightarrow X \times _{ S } S_{(q \circ f)/} \]
is a left fibration.