Quasi-abelian hearts of twin cotorsion pairs on triangulated categories

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

2 Citations (Scopus)

Abstract

We prove that, under a mild assumption, the heart H‾ of a twin cotorsion pair ((S,T),(U,V)) on a triangulated category C is a quasi-abelian category. If C is also Krull-Schmidt and T=U, we show that the heart of the cotorsion pair (S,T) is equivalent to the Gabriel-Zisman localisation of H‾ at the class of its regular morphisms. In particular, suppose C is a cluster category with a rigid object R and [XR] the ideal of morphisms factoring through XR=Ker(HomC(R,−)), then applications of our results show that C/[XR] is a quasi-abelian category. We also obtain a new proof of an equivalence between the localisation of this category at its class of regular morphisms and a certain subfactor category of C.

Original languageEnglish
JournalJournal of Algebra
Volume534
Pages (from-to)313-338
Number of pages26
ISSN0021-8693
DOIs
Publication statusPublished - 15 Sept 2019
Externally publishedYes

Keywords

  • Cluster category
  • Heart
  • Localisation
  • Quasi-abelian category
  • Triangulated category
  • Twin cotorsion pair

Fingerprint

Dive into the research topics of 'Quasi-abelian hearts of twin cotorsion pairs on triangulated categories'. Together they form a unique fingerprint.

Cite this