Cotorsion Pairs on m-term Subcategories

Abstract

Let \({\cal C}\) be a triangulated category. We define m-term subcategories on \({\cal C}\) induced by n-rigid subcategories, which are extriangulated subcategories of \({\cal C}\). Then we give a one-to-one correspondence between cotorsion pairs on 2-term subcategories \({\cal G}\) and support τ-tilting subcategories on an abelian quotient of \({\cal G}\). If an m-term subcategory is induced by a co-t-structure, then we have a one-to-one correspondence between cotorsion pairs on it and cotorsion pairs on \({\cal C}\) under certain conditions.