2025/02/12 by Afshar, Behnam, Ameri, Reza
#18D35 #20N20 #35A27 #FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2502.17466
For a hypergroup (H,∘) we consider γ∗, as the smallest equivalence relation on H such that the quotion (H/γ∗,\tiny⊗) is an abelian group. We study some more properties of γ∗. Initially, it is investigated which subhypergroup the congruence relation modulo is strongly regular on, and its quotient results in an abelian group? This is directly related to the fundamental relation γ∗, since such subhypergroups must contain Sγ. Then, we examine the functor γ∗ from a categorical perspective and investigate properties such as continuity and cocontinuity concerning it using the decomposition γ=δ\tiny∗β. For this purpose, we define the reduced words on strongly regular hypergroups. This has a direct application in studying how the functor γ∗ affects on the stalks of the sheaves of hypergroups.