English

General heart construction for twin torsion pairs on triangulated categories

Category Theory 2011-11-09 v1

Abstract

In our previous article, we constructed an abelian category from any torsion pair on a triangulated category. This generalizes the heart of a tt-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.

Keywords

Cite

@article{arxiv.1111.1820,
  title  = {General heart construction for twin torsion pairs on triangulated categories},
  author = {Hiroyuki Nakaoka},
  journal= {arXiv preprint arXiv:1111.1820},
  year   = {2011}
}

Comments

18 pages