Peter Jorgensen
Published 2021-09-03Version 1
In the theory of triangulated categories, we propose to replace hearts of $t$-structures by proper abelian subcategories, which may be plentiful even when hearts are not. For instance, this happens in negative cluster categories. In support of our proposal, we show that proper abelian subcategories with a few vanishing negative self extensions permit a tilting theory which is a direct generalisation of Happel-Reiten-Smal{\o} tilting of hearts.
Filtrations of torsion classes in proper abelian subcategories
$τ$-Tilting Theory and $τ$-Slices
Intervals of $s$-torsion pairs in extriangulated categories with negative first extensions
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