A simultaneous generalization of mutation and recollement on a triangulated category

Abstract

In this article, we introduce the notion of concentric twin cotorsion pair on a triangulated category. This notion contains the notions of tstructure, 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.

The realization of Verdier quotients as triangulated subfactors

“…We thank Dong Yang for informing us their recent analogous results in [8] and Nakaoka's results in [11]. In fact, we can deduce their results from the our main result directly; see Remark 4.8.…”