Triangulated Quotient Categories |
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Authors: | Yu Liu |
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Institution: | Department of Mathematical Sciences , Tsinghua University , Beijing 100084 , P. R. China |
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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. |
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Keywords: | Mutation Quotient triangulated category Right triangulated category |
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