Corollary 4.4.2.5. Let $q: X \rightarrow S$ and $g: B \rightarrow S$ be morphisms of simplicial sets. If $q$ is either a left fibration or a right fibration, then the simplicial set $\operatorname{Fun}_{/S}(B,X)$ is a Kan complex.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. Apply Corollary 4.4.2.4 in the special case $A = \emptyset $. $\square$