$\DeclareMathOperator{\Hom}{Hom}$ I'm struggling on understading Weibel, p.283
He said in The Bar Resolution 8.6.12,
... Since the homotopy groups of the simplicial $R$-module $\bot_* M$ may be computed using the underlying simplicial $k$-module $U(\bot_* M)$, ...
At first, the homotopy group is just homology on the complex because the category of $R$-module and $k$-module is an abelian category. So, we could just focused on the morphisms to understand. (This is from Dold-Kan correspondence and the properties on abelian categories. Actually, this is not enough to explain why.. I think this is too long to explain every detail.)
From the above conclusion, I think this is because the differentials on $\bot_* M$ is actually $k$-module morphism by following isomorphism, $d \in \Hom_R(R \otimes_k R \otimes_k \bot_* M, R \otimes_k \bot_* M) \cong \Hom_k(R \otimes_k \bot_* M, \bot_* M)$.
Do I correctly understand what he said?