Galois Connections and Preradicals in Abelian Categories
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_ | 1866911176547368960 |
|---|---|
| author | Fernández-Alonso, Rogelio Magaña, Janeth Sandoval-Miranda, Martha Lizbeth Shaid Santiago-Vargas, Valente |
| author_facet | Fernández-Alonso, Rogelio Magaña, Janeth Sandoval-Miranda, Martha Lizbeth Shaid Santiago-Vargas, Valente |
| contents | In this paper we define operations of preradicals of any abelian category. We define idempotent preradicals and radicals. We prove that every adjoint pair between abelian categories induces a Galois connection between the corresponding ordered collections of preradicals. If the abelian categories are bicomplete, we construct alpha and omega preradicals and study their respective preservation under the Galois connection. If a bicomplete abelian category is in addition locally small, then the corresponding collection of preradicals is a complete lattice. The Galois connection induced by an adjoint pair between locally small bicomplete abelian categories preserves, respectively, idempotent preradicals and radicals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Galois Connections and Preradicals in Abelian Categories Fernández-Alonso, Rogelio Magaña, Janeth Sandoval-Miranda, Martha Lizbeth Shaid Santiago-Vargas, Valente Category Theory 06A15, 18A40, 18E40, 18E05 In this paper we define operations of preradicals of any abelian category. We define idempotent preradicals and radicals. We prove that every adjoint pair between abelian categories induces a Galois connection between the corresponding ordered collections of preradicals. If the abelian categories are bicomplete, we construct alpha and omega preradicals and study their respective preservation under the Galois connection. If a bicomplete abelian category is in addition locally small, then the corresponding collection of preradicals is a complete lattice. The Galois connection induced by an adjoint pair between locally small bicomplete abelian categories preserves, respectively, idempotent preradicals and radicals. |
| title | Galois Connections and Preradicals in Abelian Categories |
| topic | Category Theory 06A15, 18A40, 18E40, 18E05 |
| url | https://arxiv.org/abs/2509.21564 |