A homotopy theory of Nakaoka twin cotorsion pairs

Abstract

We show that the Verdier quotients can be realized as subfactors by the homotopy theory of additive categories with suspensions developed in \cite{ZWLi2, ZWLi3}. As applications, we develop the homotopy theory of Nakaoka twin cotorsion pairs of triangulated categories and prove that Iyama-Yoshino triangulated subfactors are Verdier quotients under suitable conditions.

We combine it with arXiv:1612.08340

References in corpus (5)

• A simultaneous generalization of mutation and recollement on a triangulated category
• A homotopy theory of additive categories with suspensions
• The triangulation of the subfactor categories of additive categories with suspensions
• Relative singularity categories, Gorenstein objects and silting theory
• The realization of Verdier quotients as triangulated subfactors