Kerodon

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

Corollary 3.2.6.3. Let $f: (X,x) \rightarrow (Y,y)$ be a morphism of pointed Kan complexes, and suppose that the underlying morphism of simplicial sets $X \rightarrow Y$ is a homotopy equivalence. Then, for every nonnegative integer $n \geq 0$, the induced map $\pi _{n}(X,x) \rightarrow \pi _{n}(Y,y)$ is a bijection.