Corollary 4.3.7.17. Let $q: X \rightarrow S$ be a trivial Kan fibration of simplicial sets and let $f: K \rightarrow X$ be any morphism of simplicial sets. Then the induced maps
\[ X_{/f} \rightarrow S_{/ (q \circ f)} \quad \quad X_{f/} \rightarrow S_{(q \circ f)/} \]
are trivial Kan fibrations.