Corollary 3.5.9.28. Let $X$ be an $n$-truncated Kan complex. Then, for any simplicial set $B$, the Kan complex $\operatorname{Fun}(B,X)$ is also $n$-truncated.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Corollary 3.5.9.28. Let $X$ be an $n$-truncated Kan complex. Then, for any simplicial set $B$, the Kan complex $\operatorname{Fun}(B,X)$ is also $n$-truncated.
Proof. Apply Corollary 3.5.9.25 in the special case $A = \emptyset $ (or Corollary 3.5.9.27 in the special case $Y = \Delta ^0$). $\square$