forgetful functor from Ab to Grp

The forgetful functor from Category Ab to category Group is defined as functor

\begin{align*} \mathrm{ForgetGrp}: \mathrm{Ab} \rightarrow& \mathrm{Grp} \\ G \mapsto& G \\ (\varphi: G \rightarrow H) \mapsto& (\varphi: G \rightarrow H) \end{align*}