Filtrations of torsion classes in proper abelian subcategories

2024/06/19 by Kortegaard, Anders S.
#18E10 #18G80 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2406.13418

Abstract

In an abelian category \mathscrA, we can generate torsion pairs from tilting objects of projective dimension ≤ 1. However, when we look at tilting objects of projective dimension 2, there is no longer a natural choice of an associated torsion pair. Instead of trying to generate a torsion pair, Jensen, Madsen and Su generated a triple of extension closed classes that can filter any objects of \mathscrA. We generalize this result to proper abelian subcategories.

Related

• Torsion pairs and filtrations in abelian categories with tilting objects
• Universal Extensions and Ext-Orthogonal Complements of Torsion Classes
• Filtrations in abelian categories with a tilting object of homological dimension two
• Intervals of torsion pairs and generalized Happel-Reiten-Smalø tilting
• Torsion-simple objects in abelian categories