Let $G$ be a finite group.
In their paper Some Remarks On the Structure of Mackey functors , Greenlees and May define a functor:
$R: GMod \rightarrow M[G]$ where $GMod$ is the category of finite left $G$-modules and $M[G]$ is the category of $G$ Mackey functors by:
$RV(G/H) = V^H$ where $V^H= \{v\in V| h(v) = v \hspace{.2cm} \forall h\in H\}$ and $V$ is a $G$ module.
Question: In Theorem 12, why are $coker(\eta)$ and $ker(\eta)$ in $\mathcal{A}$?