# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

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 $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ is exponentiable, it suffices to verify condition $(\ast )$ in the special case where $\overline{F}: \operatorname{\mathcal{C}}'' \rightarrow \operatorname{\mathcal{C}}'$ is the inner horn $\Lambda ^{2}_{1} \hookrightarrow \Delta ^2$ (see Proposition ).