Remark 4.5.9.11. We will be primarily interested in the special case of Definition 4.5.9.10 where $U$ is an inner fibration of simplicial sets. In this case, Definition 4.5.9.10 can be considerably simplified: to show that an inner fibration of simplicial sets $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{B}}$ is exponentiable, it suffices to verify condition $(\ast )$ in the special case where $\overline{F}: \operatorname{\mathcal{B}}'' \rightarrow \operatorname{\mathcal{B}}'$ is the inner horn $\Lambda ^{2}_{1} \hookrightarrow \Delta ^2$ (see Proposition 
).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$