If G and H are two partially ordered groups, a map from G to H is a morphism of partially ordered groups if it is both a group homomorphism and a monotonic function. The partially ordered groups, together with this notion of morphism, form a category.
If G and H are two partially ordered groups a map from G to H is a morphism of partially ordered groups if it is both a group homomorphism and a monotonic function The partially ordered groups together with this notion of morphism form a category