# Kerodon

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

Corollary 4.4.5.6. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an isofibration of $\infty$-categories. For every simplicial set $B$, the induced map $\operatorname{Fun}(B, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}(B, \operatorname{\mathcal{D}})$ is also an isofibration of $\infty$-categories.

Proof. Apply Proposition 4.4.5.1 in the special case $A = \emptyset$. $\square$