Exercise 3.5.4.8. Let $A_{\ast }$ be a chain complex of abelian groups and let $n \geq -1$ be an integer. Show that the Eilenberg-MacLane space $\mathrm{K}(A_{\ast } )$ is weakly $n$-coskeletal if and only if it satisfies the following conditions:
The abelian groups $A_{m}$ vanish for $m \geq n+2$.
The differential $\partial : A_{n+1} \rightarrow A_{n}$ is a monomorphism.
Compare with Proposition 3.5.3.9.