Triangulated quotient categories arising from extriangulated categories

Abstract

In this paper, we give a common framework for constructing triangulated quotient categories from extriangulated categories. To be precise,assume that $X$ and $A$, where $X~\\subseteq~A$, are two subcategories of an extriangulated category $\\C$ satisfying certain conditions. Then $\\A/[\\X]$ is a triangulated category.This result unifies a result by Iyama and Wemyss (2013) for triangulated categories and a result by Zhou and Zhu (2018) for extriangulated categories.