Corollary 3.5.6.15. Let $X$ be a Kan complex, let $n$ be a nonnegative integer, and let $\pi _{\leq n}(X)$ be as in Construction 3.5.6.10. Then the quotient map $\operatorname{cosk}_{n+1}(X) \twoheadrightarrow \pi _{\leq n}(X)$ is a trivial Kan fibration of simplicial sets.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$