Remark 3.2.7.3. For the equivalences $(1) \Leftrightarrow (2) \Leftrightarrow (4)$ of Proposition 3.2.7.2, it is not necessary to assume that $X$ and $Y$ are Kan complexes. See Proposition 3.3.7.6.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Remark 3.2.7.3. For the equivalences $(1) \Leftrightarrow (2) \Leftrightarrow (4)$ of Proposition 3.2.7.2, it is not necessary to assume that $X$ and $Y$ are Kan complexes. See Proposition 3.3.7.6.