Definition:G-Module Homomorphism

Definition
Let $(G,\cdot)$ be a group and; let $(V,\phi)$ and $(W,\mu)$ be $G$-modules.

Then a linear mapping $f:V\to W$ is called a $G$-module homomorphism if $\forall g\in G,\ \forall v\in V;\ f(\phi(g,v))=\mu(g,f(v))$