On tilted Giraud subcategories

TL;DR

This paper introduces a method to transfer torsion pairs between abelian categories and their Giraud subcategories, establishing a correspondence with their tilted counterparts in derived categories.

Contribution

It develops a new technique to relate Giraud subcategories of an abelian category and its tilt via adjoint functors, enhancing understanding of their structural connections.

Findings

Established a correspondence between Giraud subcategories of C and H(C)

Provided a technique to move torsion pairs via adjoint functors

Applied the method to develop new insights into t-structures and derived categories

Abstract

Firstly we provide a technique to move torsion pairs in abelian categories via adjoint functors and in particular through Giraud subcategories. We apply this point in order to develop a correspondence between Giraud subcategories of an abelian category $C$ and those of its tilt $H(C)$ i.e., the heart of a t-structure on $D(C)$ induced by a torsion pair.