Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories

Souheila Hassoun, Amit Shah*

*Corresponding author for this work

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

Abstract

It was shown recently that the heart (Formula presented.) of a twin cotorsion pair (Formula presented.) on an extriangulated category is semi-abelian. We provide a sufficient condition for the heart to be integral and another for the heart to be quasi-abelian. This unifies and improves the corresponding results for exact and triangulated categories. Furthermore, if (Formula presented.) then we show that the Gabriel-Zisman localization of (Formula presented.) at the class of its regular morphisms is equivalent to the heart of the single twin cotorsion pair (Formula presented.) This generalizes and improves the known result for triangulated categories, thereby providing new insights in the exact setting.

Original languageEnglish
JournalCommunications in Algebra
Pages (from-to)1-21
Number of pages21
ISSN0092-7872
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Extriangulated category
  • heart
  • integral category
  • localization
  • quasi-abelian category
  • twin cotorsion pair

Fingerprint

Dive into the research topics of 'Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories'. Together they form a unique fingerprint.

Cite this