Functors Associated to Relations on Hypergroups and Hypermodules

If H is a strongly regular hypergroup, we show that the set of regular relations on H and the set of subhypergroups containing $0_H$ are two lattices that are isomorphic to each other. In the next step, we introduce and study the properties of functors that are constructed by a sequence of strongly regular relations. This helps us to define a specific type of free objects and tensor products on the category of regular hypergroups.