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Corollary 4.5.9.19. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{B}}$ be an exponentiable morphism of simplicial sets. For every $\infty $-category $\operatorname{\mathcal{D}}$, the projection map $\pi : \operatorname{Fun}( \operatorname{\mathcal{C}}/\operatorname{\mathcal{B}}, \operatorname{\mathcal{D}}) \rightarrow \operatorname{\mathcal{B}}$ is an isofibration of simplicial sets.

Proof. Apply Proposition 4.5.9.18 in the special case $\operatorname{\mathcal{E}}= \Delta ^0$ (see Example 4.5.9.4). $\square$