Warning 5.4.3.2. In the situation of Proposition 5.4.3.1, the projection maps
\[ \operatorname{\mathcal{C}}_{f/} \rightarrow \operatorname{\mathcal{C}}\quad \quad \operatorname{\mathcal{C}}_{/f} \rightarrow \operatorname{\mathcal{C}} \]
are generally not inner fibrations of simplicial sets.