Kerodon

Warning 3.2.2.19. Let $X$ be a Kan complex and let $n > 0$ be an integer. It follows from Example 3.2.2.18 that if two vertices $x,y \in X$ belong to the same connected component of $X$, then the homotopy groups $\pi _{n}(X,x)$ and $\pi _{n}(X,y)$ are isomorphic. Beware that, in general, there is no canonical isomorphism between $\pi _{n}(X,x)$ and $\pi _{n}(X,y)$: the isomorphism constructed in Example 3.2.2.18 depends on (the homotopy class) of the chosen edge $e: x \rightarrow y$.