Example 3.2.4.7. Let $(X,x)$ be a pointed Kan complex, let $n > 0$ be a positive integer, and let $\sigma : \Delta ^ n / \operatorname{\partial \Delta }^ n \rightarrow (X,x)$ be a morphism of pointed simplicial sets. Then $\sigma $ is nullhomotopic (in the sense of Definition 3.2.4.5) if and only if the pointed homotopy class $[\sigma ]$ is equal to the identity element in the homotopy group $\pi _{n}(X,x)$. See Proposition 3.2.1.15.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$