Remark 4.8.9.3. In the situation of Definition 4.8.9.2, we can assume without loss of generality that the functor $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is an isofibration (see Corollary 4.5.2.23). Replacing $\operatorname{\mathcal{C}}$ by the simplicial set $\mathrm{h}_{\mathit{\leq n-1}}\mathit{(\operatorname{\mathcal{C}}/\operatorname{\mathcal{D}})}$, we can further arrange that the isofibration $U$ is $(n-1)$-categorical (Proposition 4.8.8.22).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$