Example 4.7.8.3. Let $\kappa $ be an uncountable regular cardinal and let $X$ be a Kan complex. Then $X$ is locally $\kappa $-small if and only if, for every vertex $x \in X$ and every integer $n > 0$, the homotopy group $\pi _{n}(X,x)$ is $\kappa $-small.
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