Corollary 4.1.4.3. Let $q: X \rightarrow S$ be an inner fibration of simplicial sets and let $B$ be an arbitrary simplicial set. Then composition with $q$ induces an inner fibration $\operatorname{Fun}(B,X) \rightarrow \operatorname{Fun}(B,S)$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Proposition 4.1.4.1 in the special case $A = \emptyset $. $\square$