Polygroup objects in regular categories
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-03-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024552?viewType=HTML |
| _version_ | 1797219398907330560 |
|---|---|
| author | Alessandro Linzi |
| author_facet | Alessandro Linzi |
| author_sort | Alessandro Linzi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T12:33:01Z |
| format | Article |
| id | doaj.art-88d9858748b94e92bb1882c0c5378db0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T12:33:01Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-88d9858748b94e92bb1882c0c5378db02024-04-08T01:24:06ZengAIMS PressAIMS Mathematics2473-69882024-03-0195112471127710.3934/math.2024552Polygroup objects in regular categoriesAlessandro Linzi 0Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, SloveniaWe 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.https://www.aimspress.com/article/doi/10.3934/math.2024552?viewType=HTMLpolygroupcanonical hypergroupmultiringkrasner hyperringregular categoryrelation |
| spellingShingle | Alessandro Linzi Polygroup objects in regular categories AIMS Mathematics polygroup canonical hypergroup multiring krasner hyperring regular category relation |
| title | Polygroup objects in regular categories |
| title_full | Polygroup objects in regular categories |
| title_fullStr | Polygroup objects in regular categories |
| title_full_unstemmed | Polygroup objects in regular categories |
| title_short | Polygroup objects in regular categories |
| title_sort | polygroup objects in regular categories |
| topic | polygroup canonical hypergroup multiring krasner hyperring regular category relation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024552?viewType=HTML |
| work_keys_str_mv | AT alessandrolinzi polygroupobjectsinregularcategories |