Fundamental Functor on Hypergroups
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916628724187136 |
|---|---|
| author | Afshar, Behnam Ameri, Reza |
| author_facet | Afshar, Behnam Ameri, Reza |
| contents | For a hypergroup $(H,\circ)$ we consider $γ^{\ast}$, as the smallest equivalence relation on $H$ such that the quotion $(H/γ^{\ast},\tiny{\otimes})$ is an abelian group. We study some more properties of $γ^{\ast}$. 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 $γ^{\ast}$, since such subhypergroups must contain $S_γ$. Then, we examine the functor $γ^{\ast}$ from a categorical perspective and investigate properties such as continuity and cocontinuity concerning it using the decomposition $γ=δ\tiny{\ast}β$. For this purpose, we define the reduced words on strongly regular hypergroups. This has a direct application in studying how the functor $γ^{\ast}$ affects on the stalks of the sheaves of hypergroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental Functor on Hypergroups Afshar, Behnam Ameri, Reza General Mathematics 20N20, 18D35, 35A27 For a hypergroup $(H,\circ)$ we consider $γ^{\ast}$, as the smallest equivalence relation on $H$ such that the quotion $(H/γ^{\ast},\tiny{\otimes})$ is an abelian group. We study some more properties of $γ^{\ast}$. 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 $γ^{\ast}$, since such subhypergroups must contain $S_γ$. Then, we examine the functor $γ^{\ast}$ from a categorical perspective and investigate properties such as continuity and cocontinuity concerning it using the decomposition $γ=δ\tiny{\ast}β$. For this purpose, we define the reduced words on strongly regular hypergroups. This has a direct application in studying how the functor $γ^{\ast}$ affects on the stalks of the sheaves of hypergroups. |
| title | Fundamental Functor on Hypergroups |
| topic | General Mathematics 20N20, 18D35, 35A27 |
| url | https://arxiv.org/abs/2502.17466 |