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Gorenstein dimension of abelian categories arising from cluster tilting subcategories

Yu Liu, Panyue Zhou (2021)

Czechoslovak Mathematical Journal

Let 𝒞 be a triangulated category and 𝒳 be a cluster tilting subcategory of 𝒞 . Koenig and Zhu showed that the quotient category 𝒞 / 𝒳 is Gorenstein of Gorenstein dimension at most one. But this is not always true when 𝒞 becomes an exact category. The notion of an extriangulated category was introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. Now let 𝒞 be an extriangulated category with enough projectives and enough injectives, and 𝒳 a cluster...

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