Remark 3.2.8.2. In the situation of Proposition 3.2.8.1, the assumption that $S$ and $S'$ are Kan complexes can be eliminated at the cost of working with weak homotopy equivalences in place of homotopy equivalences: see Proposition 3.3.7.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$