Remark 4.8.6.30. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets. It follows from Example 4.8.6.26 and Remark 4.8.6.29 that if $F$ is an $n$-categorical inner fibration, then the fiber $\operatorname{\mathcal{C}}_{D} = \{ D\} \times _{\operatorname{\mathcal{D}}} \operatorname{\mathcal{C}}$ is an $(n,1)$-category for each vertex $D \in \operatorname{\mathcal{D}}$. Beware that the converse is generally false.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$