Remark 3.1.2.8. Let $f: X \rightarrow S$ be a Kan fibration of simplicial sets. If $f$ is surjective on vertices, then it is surjective on $n$-simplices for every integer $n \geq 0$. This follows from the lifting property of Remark 3.1.2.7, combined with the observation that the inclusion map $\{ 0\} \hookrightarrow \Delta ^ n$ is anodyne (Example 3.1.2.5).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$