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Polygroup objects in regular categories
Alessandro Linzi, 2024, original scientific article


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: 374; Downloads: 3
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From HX-groups to HX-polygroups
Seyed 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: 725; Downloads: 7
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On Factorizable Semihypergroups
Dariush Heidari, Irina Elena Cristea, 2020, original scientific article

Keywords: semihypergroup, factorization, regular semihypergroup, polygroup
Published in RUNG: 01.07.2020; Views: 2373; Downloads: 77
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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: 2547; Downloads: 0
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Subpolygroups related to a fuzzy topology
N. Abbasizadeh, Irina Elena Cristea, Bijan Davvaz, Jianming Zhan, 2018, original scientific article

Keywords: polygroup, fuzzy topological space, (relatively) fuzzy continuity, lower (upper) fuzzy topological subpolygroup
Published in RUNG: 21.08.2018; Views: 3446; Downloads: 0
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Left almost polygroups
Naveed Yaqoob, Irina Elena Cristea, Muhhamad Gulistan, Shah Nawaz, 2018, original scientific article

Abstract: In this introductory note we define the concept of left almost polygroup and provide several examples. We also discuss the quotient structure and isomorphism theorems for left almost polygroups.
Keywords: left almost polygroup, direct product, hyperorder, homomorphism
Published in RUNG: 28.03.2018; Views: 3832; Downloads: 0
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