Example 3.5.7.10. Let $n \geq -1$ be an integer and let $A_{\ast }$ be a chain complex of abelian groups. Then the Eilenberg-MacLane space $\mathrm{K}(A_{\ast } )$ is $n$-truncated if and only if the homology groups $\mathrm{H}_{m}(A)$ vanish for $m > n$ (see Exercise 3.2.2.22).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$