Direct Limit of (m, n)-ary Hypermodules

The purpose of this paper is the study of direct limit in the category of (m,n)-ary hypermodules over (m,n)-hyperring R. In this regards, we introduce and study R(m,n) − Hmod, the category of R(m,n) − Hmod, and direct limit in this category. In particular, we study a direct limit of morphisms, direct systems of kernels, and cokernels. Finally, we investigate the relationship between the functor home and direct limit and prove that the functor hom preserves direct limit in category R(m,n) − Hmod.