Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 3.1.5.4. Let $f: X_{} \rightarrow Y_{}$ be a morphism of Kan complexes. If $f$ is a homotopy equivalence, then the induced map of fundamental groupoids $\pi _{\leq 1}(f): \pi _{\leq 1}(X) \rightarrow \pi _{\leq 1}(Y)$ is an equivalence of categories. In particular, $f$ induces a bijection $\pi _0(f): \pi _0( X_{} ) \rightarrow \pi _0( Y_{} )$.