Hearts of twin cotorsion pairs revisited: integral and abelian hearts

TL;DR

This paper investigates the properties of hearts of twin cotorsion pairs, establishing conditions under which these hearts are integral or abelian, thus clarifying their algebraic structure.

Contribution

It provides a necessary and sufficient condition for the hearts of twin cotorsion pairs to be integral or abelian, advancing understanding of their algebraic properties.

Findings

Hearts of twin cotorsion pairs are quasi-abelian.

They are not always integral.

Conditions for integrality and abelianness are established.

Abstract

Hearts of twin cotorsion pairs are shown to be quasi-abelian. But they are not always integral. In this article, we provide a sufficient and necessary condition for the hearts of twin cotorsion pairs being integral (resp. abelian).