A Simultaneous Generalization of Mutation and Recollement of Cotorsion Pairs on a Triangulated Category

摘要

In this article, we introduce the notion of concentric twin cotorsion pair on a triangulated category. This notion contains the notions of t-structure, cluster tilting subcategory, co-t-structure and functorally finite rigid subcategory as examples. Moreover, a recollement of triangulated categories can be regarded as a special case of concentric twin cotorsion pair. To any concentric twin cotorsion pair, we associate a pretriangulated subquotient category. This enables us to give a simultaneous generalization of the Iyama-Yoshino reduction and the recollement of cotorsion pairs. This allows us to give a generalized mutation on cotorsion pairs defined by the concentric twin cotorsion pair.