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.

we rewrite the section 6 and introduce the notions of Frobenius partial one-sided triangulated categories

References in corpus (2)

• A homotopy theory of additive categories with suspensions
• Frobenius condition on a pretriangulated category, and triangulation on the associated stable category

Cited by in corpus (5)

• A homotopy theory of additive categories with suspensions
• The realization of Verdier quotients as triangulated subfactors
• Right triangulated categories: As extriangulated categories, aisles and co-aisles
• $n$-abelian quotient categories
• A homotopy theory of Nakaoka twin cotorsion pairs