1. Polygroup objects in regular categoriesAlessandro Linzi, 2024, original scientific article Abstract: We express the fundamental properties of commutative polygroups (also known as canonical hypergroups) in category-theoretic terms, over the category $ \mathbf{Set} $ formed by sets and functions. For this, we employ regularity as well as the monoidal structure induced on the category $ {\mathbf{Rel}} $ of sets and relations by cartesian products. We highlight how our approach can be generalised to any regular category. In addition, we consider the theory of partial multirings and find fully faithful functors between certain slice or coslice categories of the category of partial multirings and other categories formed by well-known mathematical structures and their morphisms.
Keywords: polygroup, canonical hypergroup, multiring, Krasner hyperring, regular category, relation
Published in RUNG: 25.03.2024; Views: 2933; Downloads: 8
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2. From HX-groups to HX-polygroupsSeyed S. Mousavi, Morteza Jafarpour, Irina Elena Cristea, 2023, original scientific article Keywords: HX-group, hypercompositional structure, coset, polygroup, regularity, uniformity, essentiality, double coset
Published in RUNG: 22.12.2023; Views: 2468; Downloads: 8
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3. Iranmanesh, Mahdeyeh; Jafarpour, Morteza; Aghabozorgi, Hossien; Zhan, Jian Ming Classification of Krasner hyperfields of order 4. Acta Math. Sin. (Engl. Ser.) 36 (2020), no. 8, 889–902.Irina Elena Cristea, 2022, review, book review, critique Keywords: Krasner hyperfield, polygroup, order, Matlab
Published in RUNG: 11.05.2022; Views: 2690; Downloads: 0
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5. Heidari, D.[Heidari, Dariush](IR-MIHES);Davvaz, B.[Davvaz, Bijan](IR-YAZD-M)Characterization of small polygroups by their fundamental groups.2020, review, book review, critique Keywords: Maple, polygroup, isomorphism, fundamental group
Published in RUNG: 06.04.2020; Views: 3842; Downloads: 0
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