Revising Auslander-Gruson-Jensen duality
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910223237644288 |
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| author | Ebrahimi, Ramin Hafezi, Rasool Wei, Jiaqun |
| author_facet | Ebrahimi, Ramin Hafezi, Rasool Wei, Jiaqun |
| contents | For a ring $A$ there is a well-known duality between definable subcategories of right $A$-modules and definable subcategories of left $A$ modules. This is a consequence of Auslander-Gruson-Jensen duality $\rm mod\text{-}(mod\text{-}A)\rightarrow mod\text{-}(mod\text{-}A^{op})$. The existence of this duality arises from the fact that $\rm mod\text{-}(mod\text{-}A)$ is the free abelian category over the pre-additive category $A$ with a single object.
In this note, first, we give a simple description of the free abelian category. This description clarifies Auslender-Gruson-Jensen duality and also the duality between definable subcategories of right $A$-modules and those of left $A$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revising Auslander-Gruson-Jensen duality Ebrahimi, Ramin Hafezi, Rasool Wei, Jiaqun Representation Theory Category Theory Rings and Algebras For a ring $A$ there is a well-known duality between definable subcategories of right $A$-modules and definable subcategories of left $A$ modules. This is a consequence of Auslander-Gruson-Jensen duality $\rm mod\text{-}(mod\text{-}A)\rightarrow mod\text{-}(mod\text{-}A^{op})$. The existence of this duality arises from the fact that $\rm mod\text{-}(mod\text{-}A)$ is the free abelian category over the pre-additive category $A$ with a single object. In this note, first, we give a simple description of the free abelian category. This description clarifies Auslender-Gruson-Jensen duality and also the duality between definable subcategories of right $A$-modules and those of left $A$-modules. |
| title | Revising Auslander-Gruson-Jensen duality |
| topic | Representation Theory Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2605.03458 |