Half exact functors associated with cotorsion pairs on exact categories

TL;DR

This paper constructs a half exact functor from an exact category to its heart, extending previous work on cotorsion pairs and providing conditions for equivalence of different hearts.

Contribution

It introduces a new half exact functor for cotorsion pairs on exact categories, generalizing triangulated category constructions and analyzing heart equivalences.

Findings

Constructed a half exact functor from an exact category to its heart.

Provided sufficient conditions for equivalence of different hearts.

Extended the framework of cotorsion pairs to new categorical contexts.

Abstract

In the previous article "Hearts of twin cotorsion pairs on exact categories", we introduced the notion of the heart for any cotorsion pair on an exact category with enough projectives and injectives, and showed that it is an abelian category. In this paper, we construct a half exact functor from the exact category to the heart. This is analog of the construction of Abe and Nakaoka for triangulated categories. We will also use this half exact functor to find out a sufficient condition when two different hearts are equivalent.