Corollary 3.5.9.22. Let $X$ be a Kan complex and let $n \geq -2$ be an integer. Then $X$ is $n$-truncated if and only if the diagonal map $X \rightarrow \operatorname{Fun}( \operatorname{\partial \Delta }^{n+2}, X)$ is a homotopy equivalence.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$