Coherent and ideal actions in ideally exact categories
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917524081213440 |
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| author | Mancini, Manuel Metere, Giuseppe Piazza, Federica |
| author_facet | Mancini, Manuel Metere, Giuseppe Piazza, Federica |
| contents | In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of rings and algebras. We prove that every ideal action is coherent, and that the converse statement holds in some relevant ideally exact contexts. Furthermore, a connection with G. Janelidze's notion of semidirect product in ideally exact categories is analysed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coherent and ideal actions in ideally exact categories Mancini, Manuel Metere, Giuseppe Piazza, Federica Category Theory Logic Rings and Algebras 03B52, 06D35, 08C05, 16B50, 18C05, 18E13 In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of rings and algebras. We prove that every ideal action is coherent, and that the converse statement holds in some relevant ideally exact contexts. Furthermore, a connection with G. Janelidze's notion of semidirect product in ideally exact categories is analysed. |
| title | Coherent and ideal actions in ideally exact categories |
| topic | Category Theory Logic Rings and Algebras 03B52, 06D35, 08C05, 16B50, 18C05, 18E13 |
| url | https://arxiv.org/abs/2507.06124 |