Filtrations of torsion classes in proper abelian subcategories

Abstract

In an abelian category $\mathcal{A}$, we can generate torsion pairs from tilting objects of projective dimension $\le 1$. 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 $\mathcal{A}$. We generalize this result to proper abelian subcategories.

12 pages, comments are welcome