Proposition 3.5.9.8. Let $f: X \rightarrow Y$ be a Kan fibration between Kan complexes and let $n$ be an integer. Then $f$ is $n$-truncated (in the sense of Definition 3.5.9.1) if and only if, for each vertex $y \in Y$, the Kan complex $X_{y} = \{ y\} \times _{Y} X$ is $n$-truncated (in the sense of Definition 3.5.7.1).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$