Title: 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.