Universal Extensions and Ext-Orthogonal Complements of Torsion Classes
Abstract
We show that torsion pairs in Krull--Schmidt abelian categories induce an equivalence between the subcategory of torsion-free objects admitting universal extensions to the torsion subcategory, and a quotient of the ext-orthogonal complement of the torsion subcategory. This generalize an equivalence described by Bauer--Botnan--Oppermann--Steen for tilting-torsion pairs and by Buan--Zhou for functorially finite torsion pairs. The result also provides a more direct proof of the functorially finite case, not relying on the machinery of two-term silting complexes. We illustrate our result in the special case of tube categories.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2024
- DOI:
- 10.48550/arXiv.2410.02322
- arXiv:
- arXiv:2410.02322
- Bibcode:
- 2024arXiv241002322R
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Category Theory
- E-Print:
- 17 pages. Comments welcome