On definable subcategories
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929586541953024 |
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| author | Ebrahimi, Ramin |
| author_facet | Ebrahimi, Ramin |
| contents | Let $\mathcal{X}$ be a skeletally small additive category. Using the canonical equivalence between two different presentations of the free abelian category over $\mathcal{X}$, we give a new and simple characterization of definable subcategories of $\rm Mod\text{-}\mathcal{X}$, and in particular definable subcategories of modules over rings. In the end, we give a conceptual proof of Auslander-Gruson-Jensen duality, which makes the duality between definable subcategories of left and right module more transparent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06432 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On definable subcategories Ebrahimi, Ramin Category Theory Rings and Algebras Representation Theory Let $\mathcal{X}$ be a skeletally small additive category. Using the canonical equivalence between two different presentations of the free abelian category over $\mathcal{X}$, we give a new and simple characterization of definable subcategories of $\rm Mod\text{-}\mathcal{X}$, and in particular definable subcategories of modules over rings. In the end, we give a conceptual proof of Auslander-Gruson-Jensen duality, which makes the duality between definable subcategories of left and right module more transparent. |
| title | On definable subcategories |
| topic | Category Theory Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2411.06432 |