The sign map sgn form S_n to {+1,-1} is a group morphism.

The determinant is a morphism from the general linear group GL_n(R) to the multiplicative group R^*.

Fix an integer a. The map from Z to Z defined by n -> an is a morphism of the additive group on Z.

If H is a subgroup of a group G, then the map h H -> h G is a morphism.