Remark 2.5.6.18. Let $f: A_{\bullet } \rightarrow B_{\bullet }$ be a morphism of simplicial abelian groups. By virtue of Proposition 2.5.6.17 and Lemma 2.5.6.16, the following assertions are equivalent:
For every integer $n \geq 0$, the map of abelian groups $A_{n} \rightarrow B_ n$ is surjective (respectively split surjective, injective, split injective).
For every integer $n \geq 0$, the map of abelian groups $\mathrm{N}_{n}(A) \rightarrow \mathrm{N}_{n}(B)$ is surjective (respectively split surjective, injective, split injective).