Abelizations of weakly associative hyperstructures based on their direct squares. (English) Zbl 1110.20304

Summary: The paper contains a simple construction of some types of commutative hyperstructures as hypergroupoids, weakly associative semi-hypergroupoids, hypergroups, quasi-hypergroups and weakly associative hyperrings from non-commutative hyperstructures. It is proved that the used construction induces reflectors on suitable categories of the mentioned hyperstructures.


20N20 Hypergroups
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
16Y99 Generalizations
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