forgetful functor from RMod to Ab

Let \(R\) be a ring, then the forgetful functor from category RMod to Category Ab is defined as functor

\begin{align*} \mathrm{ForgetAb}: \mathrm{RMod} \rightarrow& \mathrm{Ab} \\ M \mapsto& M \\ (f: M \rightarrow N) \mapsto& (f: M \rightarrow N) \end{align*}