Warning 10.3.1.23. Proposition 10.3.1.22 is not a special case of Corollary 10.3.1.13, because the slice category $\operatorname{\mathcal{D}}_{/Y}$ is usually not equivalent to the homotopy category of $\operatorname{\mathcal{C}}_{/Y}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$