Stability Conditions on Abelian Comma Categories
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915585420427264 |
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| author | de Oliveira, Ellen Neulaender, Guido |
| author_facet | de Oliveira, Ellen Neulaender, Guido |
| contents | A comma category, exemplified in algebraic geometry by coherent systems, combines two categories over a third through morphisms between their objects. We establish sufficient conditions for it to be abelian, compute its Grothendieck group, and give necessary and sufficient criteria for it to be noetherian and artinian. Finally, we define a stability condition on abelian comma categories under hypotheses on the initial categories and, conversely, induce stability conditions on the initial abelian categories from those on the comma categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability Conditions on Abelian Comma Categories de Oliveira, Ellen Neulaender, Guido Category Theory Algebraic Geometry 18E10, 14F05 A comma category, exemplified in algebraic geometry by coherent systems, combines two categories over a third through morphisms between their objects. We establish sufficient conditions for it to be abelian, compute its Grothendieck group, and give necessary and sufficient criteria for it to be noetherian and artinian. Finally, we define a stability condition on abelian comma categories under hypotheses on the initial categories and, conversely, induce stability conditions on the initial abelian categories from those on the comma categories. |
| title | Stability Conditions on Abelian Comma Categories |
| topic | Category Theory Algebraic Geometry 18E10, 14F05 |
| url | https://arxiv.org/abs/2510.25450 |