$\forall$$g$, $h$:IGroup, $f$:($\mid$$g$$\mid\rightarrow\mid$$h$$\mid$). ($\forall$$a$, $b$:$\mid$$g$$\mid$. $f$($a$ $\ast$ $b$) = (($f$($a$)) $\ast$ ($f$($b$)))) $\Rightarrow$ IsMonHom\{$g$,$h$\}($f$)