Weak cotorsion, $\tau$-tilting and two-term categories

TL;DR

This paper introduces a generalized concept of cotorsion pairs linked to $ au$-tilting theory, co-t-structures, and two-term categories, expanding the framework of module and triangulated categories.

Contribution

It generalizes cotorsion pairs in module categories and explores their connections to $ au$-tilting theory, co-t-structures, and two-term categories, providing new insights into their interplay.

Findings

Established a link between generalized cotorsion pairs and $ au$-tilting theory.

Connected cotorsion pairs to co-t-structures in triangulated categories.

Introduced two-term categories as extension closed subcategories.

Abstract

Motivated by its links to $\tau$-tilting theory, we introduce a generalization of cotorsion pairs in module categories. Such pairs are also linked to co-t-structures in corresponding triangulated categories, and to cotorsion pairs in certain extension closed (and hence extriangulated) subcategories, which we call two-term categories.