# Kerodon

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Corollary 4.5.9.18. Let $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ be an exponentiable morphism of simplicial sets. For every isofibration of simplicial sets $V: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{D}}$, the projection map $\operatorname{Res}_{\operatorname{\mathcal{D}}/\operatorname{\mathcal{C}}}( \operatorname{\mathcal{E}}) \rightarrow \operatorname{\mathcal{C}}$ is also an isofibration of simplicial sets.

Proof. Applying Proposition 4.5.9.17 in the special case $\operatorname{\mathcal{E}}' = \operatorname{\mathcal{D}}$. $\square$