Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585312120200101On exact category of $(m, n)$-ary hypermodules69888079210.29252/cgasa.12.1.69ENNajmehJafarzadehDepartment of Mathematics, Payamenoor University,P.O. Box 19395-3697, Tehran, Iran.RezaAmeriMathematics, School of Mathematics, Statistics and Computer
Science, University of Tehran0000-0001-5760-1788Journal Article20170612We introduce and study category of $(m, n)$-ary hypermodules as a generalization of the category of $(m, n)$-modules as well as the category of classical modules. Also, we study various kinds of morphisms. Especially, we characterize monomorphisms and epimorphisms in this category. We will proceed to study the fundamental relation on $(m, n)$-hypermodules, as an important tool in the study of algebraic hyperstructures and prove that this relation is really functorial, that is, we introduce the fundamental functor from the category of $(m, n)$-hypermodules to the category $(m, n)$-modules and prove that it preserves monomorphisms. Finally, we prove that the category of $(m, n)$-hypermodules is an exact category, and, hence, it generalizes the classical case.https://cgasa.sbu.ac.ir/article_80792_907e526521584c03372aaada0e600e45.pdf