The triangulation of the subfactor categories of additive categories with suspensions

Abstract: We provide a framework to triangulate subfactor categories of additive categories with additive endofunctors. It is proved that such a framework is sufficiently flexible to cover many instances in algebra and geometry where abelian, exact and triangulated subfactor categories are constructed. As an application, we show that Iyama-Yoshino triangulated subfactor categories can be modeled.