Kerodon

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

Definition 3.1.5.11. Let $f: X_{} \rightarrow Y_{}$ be a morphism of simplicial sets. We will say that $f$ is a weak homotopy equivalence if, for every Kan complex $Z_{}$, precomposition with $f$ induces a bijection $\pi _0( \operatorname{Fun}(Y_{}, Z_{} ) ) \rightarrow \pi _0( \operatorname{Fun}( X_{}, Z_{} ) )$.