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.

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