Warning 4.7.4.13. The assertion of Corollary 4.7.4.12 is false in the case $\kappa = \aleph _0$. That is, if $K$ and $S$ are finite simplicial sets, then the simplicial set $\operatorname{Fun}(K, S)$ need not be finite.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$