Relative AR-correspondence, co-t-structure and silting pair

TL;DR

This paper introduces silting pairs as a generalization of tilting pairs, establishing a correspondence with certain subcategories and bounded above co-t-structures, thus advancing the understanding of their categorical relationships.

Contribution

It extends the characterization of tilting modules to silting pairs and establishes bijections with specific subcategories and co-t-structures.

Findings

Silting pairs are characterized and related to subcategories.

A bijection between silting pairs and bounded above co-t-structures is proven.

The work generalizes existing tilting theory results.

Abstract

As a generalization of tilting pair, which was introduced by Miyashita in \cite{YM}, the notion of silting pair is introduced in this paper. The authors extends a characterization of tilting modules given by Bazzoni \cite[Theorem~3.11]{BS} to silting pairs, and proves that there is an one-to-one correspondence between equivalent classes of silting pairs and certain subcategories which satisfy some conditions. Furthermore, the authors also gives a bijection between equivalent class of silting pairs and bounded above co-t-structure.