Silting objects and torsion pairs in comma categories

TL;DR

This paper characterizes silting objects and torsion pairs in comma categories, establishing conditions under which pairs in subcategories induce torsion pairs in the comma category, advancing understanding in module theory.

Contribution

It provides a new characterization of silting objects and torsion pairs in comma categories, linking subcategory pairs to torsion pairs in the comma category.

Findings

Torsion pairs in subcategories induce torsion pairs in comma categories under certain conditions.

Characterization of silting objects in comma categories.

Conditions for pairs in subcategories to form torsion pairs in the comma category.

Abstract

In this paper, we first give a characterization of silting objects in the comma category Assume that C1 and C2 are two subcategories of left R-modules, D1 and D2 be two subcategories of left S-modules. We mainly prove that (C1, C2) and (D1, D2) are torsion pairs if and only if the induced two pairs in the special comma category are torsion pairs under certain conditions.