General heart construction for twin torsion pairs on triangulated categories

Details General heart construction for twin torsion pairs on triangulated categories General heart construction for twin torsion pairs on triangulated categories

2011-11-08

arxiv.org/abs/1111.1820v1

Mathematics

Category Theory

18 pages

Scientific paper

In our previous article, we constructed an abelian category from any torsion pair on a triangulated category. This generalizes the heart of a $t$-structure and the ideal quotient by a cluster tilting subcategory. Recently, generalizing the quotient by a cluster tilting subcategory, Buan and Marsh showed that an integral preabelian category can be constructed as a quotient, from a rigid object in a triangulated category with some conditions. In this article, by considering a pair of torsion pairs, we make a simultaneous genralization of these two constructions.

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