Corollary 4.3.7.19. Let $X$ be a contractible Kan complex and let $f: K \rightarrow X$ be a morphism of simplicial sets. Then the projection maps
\[ X_{/f} \rightarrow X \quad \quad X_{f/} \rightarrow X \]
are trivial Kan fibrations. In particular, $X_{/f}$ and $X_{f/}$ are also contractible Kan complexes.