Example 4.6.2.16. Let $f: X \rightarrow Y$ be a morphism of Kan complexes. Then $f$ is essentially surjective (in the sense of Definition 4.6.2.11) if and only if the induced map $\pi _0(f): \pi _0(X) \rightarrow \pi _0(Y)$ is a surjection.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$