On categories of hypergroups and hypermodules

Abstract The purpose of this note is the study categories of hypergroups and hypermodules, especially Hv -groups and Hv -modules. In this regards, first we introduce several categories of hypergroups and hypermodules by considering various structures of hypergroups and hypermodules and various types of homomorphisms of them. Then we investigate the basic objects of these categories such as kernel, cokernel, product, coproduct and etc. Finally, we construct some functors between the categories of hypermodules and hypergroups. In particular, we consider the fundamental relation on hypergroups, hypermodules, and construct some functors from the categories of hypergroups and hypermodules to the categories of hypergroups and hypermodules.