Category:Definitions/G-Module Homomorphisms

This category contains definitions related to G-Module Homomorphisms.
Related results can be found in Category:G-Module Homomorphisms.

Let $\struct {G, \cdot}$ be a group.

Let $\struct {V, \phi}$ and $\struct {W, \mu}$ be $G$-modules.

Then a linear transformation $f: V \to W$ is called a $G$-module homomorphism if and only if:

$\forall g \in G: \forall v \in V: \map f {\map \phi {g, v} } = \map \mu {g, \map f v}$