Triangulated quotient categories

TL;DR

This paper introduces a mutation concept for subcategories in right triangulated categories, showing that certain quotient categories inherit a triangulated structure, unifying previous constructions in the field.

Contribution

It defines a mutation of subcategories in right triangulated categories and proves that their quotients can be triangulated, unifying existing theories.

Findings

The quotient category Z/D inherits a right triangulated structure.

Under certain conditions, Z/D becomes a triangulated category.

The results unify Iyama-Yoshino and J{ extbackslash o}rgensen's constructions.

Abstract

A notion of mutation of subcategories in a right triangulated category is defined in this paper. When (Z,Z) is a D-mutation pair in a right triangulated category C, the quotient category Z/D carries naturally a right triangulated structure. More-over, if the right triangulated category satisfies some reasonable conditions, then the right triangulated quotient category Z/D becomes a triangulated category. When C is triangulated, our result unifies the constructions of the quotient triangulated categories by Iyama-Yoshino and by J{\o}rgensen respectively.