Corollary 1.1.3.14. Let $k$ be an integer and let $f_{\bullet }: S_{\bullet } \rightarrow T_{\bullet }$ be a morphism between simplicial sets having dimension $\leq k$. Suppose that, for every nonnegative integer $n \leq k$, the map of sets $f_{n}: S_{n} \rightarrow T_{n}$ is a bijection. Then $f$ is an isomorphism of simplicial sets.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$