Triangulated Quotient Categories

Abstract

A notion of mutation of subcategories in a right triangulated category is defined in this article. 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. Moreover, 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 Jørgensen, respectively.

Key Words:

• Mutation
• Quotient triangulated category
• Right triangulated category

2010 Mathematics Subject Classification:

• 16G20
• 16G70
• 19S99
• 17B20

ACKNOWLEDGMENTS

The authors would like to thank the referee for his/her very useful suggestions to improve the article.

The second author was supported partly by the NSF of China (Grants 11071133, 11131001) and by in part Doctoral Program Foundation of Institute of Higher Education (2009).

Notes

Communicated by D. Zacharia.