Warning 3.5.5.15. Corollary 3.5.5.14 is not quite true in the case $n = 0$. In this case, conditions $(2)$ and $(3)$ are equivalent to each other (Proposition 3.5.1.22), but condition $(1)$ is automatically satisfied (since $Y$ is a discrete simplicial set).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$