TRIANGULATED QUOTIENT CATEGORIES

A notion of mutation of subcategories in a right triangulated category is defined in this article. When (?, ?) is a ?-mutation pair in a right triangulated category ?, the quotient category ?/? carries naturally a right triangulated structure. Moreover, if the right triangulated category satisfies some reasonable conditions, then the right triangulated quotient category ?/? becomes a triangulated category. When ? is triangulated, our result unifies the constructions of the quotient triangulated categories by Iyama-Yoshino and by JOrgensen, respectively.