Exercise 10.2.3.7. Let $n$ be an integer. Show that a simplicial abelian group $A_{\bullet }$ is $n$-skeletal (when regarded as a simplicial object of the $\infty $-category $\operatorname{N}_{\bullet }( \operatorname{ Ab })$) if and only if the normalized Moore complex
\[ \cdots \rightarrow \mathrm{N}_{2}(A) \xrightarrow {\partial } \mathrm{N}_{1}(A) \xrightarrow {\partial } \mathrm{N}_{0}(A) \]
is concentrated in degrees $\leq n$: that is, the abelian group $\mathrm{N}_{k}(A)$ vanishes for $k > n$. Beware that this condition does not guarantee that $A_{\bullet }$ is $n$-skeletal when regarded as a simplicial set.