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.