Corollary 4.5.5.15. Let $q: X \rightarrow S$ be an isofibration of simplicial sets. For every simplicial set $B$, the induced map $\operatorname{Fun}(B, X) \rightarrow \operatorname{Fun}(B,S)$ is also an isofibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 4.5.5.14 in the special case $A = \emptyset $. $\square$