Remark 3.5.9.21. In the situation of Corollary 3.5.9.20, suppose that $f$ is a Kan fibration. Then the morphism $\theta $ is also a Kan fibration (Theorem 3.1.3.1). Consequently, $f$ is $n$-truncated if and only if $\theta $ is a trivial Kan fibration (Proposition 3.2.7.2).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$