# Equivalence of the categories of group triples and of hypergroups over the group

## TL;DR

This paper proves an equivalence between the category of hypergroups over a group and the category of triples consisting of a group, a subgroup, and a transversal, establishing a fundamental structural correspondence.

## Contribution

It establishes a categorical equivalence between hypergroups over a group and triples of groups, subgroups, and transversals, revealing a deep structural connection.

## Key findings

- Categories of hypergroups over a group and triples are equivalent.
- Provides a new perspective on the structure of hypergroups.
- Bridges concepts in group theory and hyperstructure theory.

## Abstract

The main result of this paper is that the categories of (right) hypergroups over the group and of triples, consisting of a group, its subgroup and a (right) transversal to this subgroup, are equivalent.