This analysis finds isomorphism between lattices of regular relations and subhypergroups in hypergroups, suggesting new structures in mathematical categories.
If H is a strongly regular hypergroup, we show that the set of regular relations on H and the set of subhypergroups containing 0H 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.
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Afshar et al. (2025) studied this question.
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