We introduce the category of R(m, n)-hypermodules over a Krasner (m, n)-hyperring R and obtain some categorical objects in this category such as product and coproduct. We apply the fundamental relations * and * on, M and, R respectively to construct fundamental functor from the category of R(m, n)-hypermodules into category of R/*-modules. In particular we consider the fundamental relation on (m, n)-hypermodules, and construct functor from the category of (m, n)-hypermodules to the category of (m, n)-modules. Then, we find the relations between hom, product, coproduct and fundamental functor.