# Kerodon

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Corollary 4.4.5.7. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an isofibration of $\infty$-categories. For every simplicial set $B$, the induced map $\operatorname{Fun}(B, \operatorname{\mathcal{C}})^{\simeq } \rightarrow \operatorname{Fun}(B, \operatorname{\mathcal{D}})^{\simeq }$ is a Kan fibration of Kan complexes.

Proof. Combine Corollary 4.4.5.6 with Proposition 4.4.3.7. $\square$