# Kerodon

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

Corollary 1.4.5.7. Let $p: X_{\bullet } \rightarrow Y_{\bullet }$ be a trivial Kan fibration of simplicial sets. Then, for every simplicial set $B_{\bullet }$, the induced map $\operatorname{Fun}( B_{\bullet }, X_{\bullet } ) \rightarrow \operatorname{Fun}( B_{\bullet }, Y_{\bullet } )$ is a trivial Kan fibration.

Proof. Apply Corollary 1.4.5.6 in the special case $A_{\bullet } = \emptyset$. $\square$