Mathematics > Representation Theory
[Submitted on 3 Oct 2024]
Title:Universal Extensions and Ext-Orthogonal Complements of Torsion Classes
View PDFAbstract: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.
Submission history
From: Endre Sørmo Rundsveen [view email][v1] Thu, 3 Oct 2024 09:08:33 UTC (23 KB)
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