Remark 4.8.8.7. Let $f: A \rightarrow B$ be a morphism of simplicial sets. Then $f$ is a categorical equivalence if and only if it is categorically $n$-connective for every integer $n$. See Remark 4.8.5.8.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$