Corollary 8.1.1.16. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an inner fibration of simplicial sets. Then the induced map $\operatorname{Tw}(U): \operatorname{Tw}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{Tw}(\operatorname{\mathcal{D}})$ is an inner fibration. If $U$ is an isofibration, then $\operatorname{Tw}(U)$ is also an isofibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$