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arXiv · 1904.09797

Gorenstein dimension of abelian categories

Yu Liu·Panyue Zhou
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Abstract

Let C be triangulated category and X a cluster tilting subcategory of C. Koenig and Zhu showed that the quotient category C/X is Gorenstein of Gorenstein dimension at most one. 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 extriangulated category with enough projectives and enough injectives, and X a cluster tilting subcategory of C. In this article, we show that under certain conditions the quotient category C/X is Gorenstein of Gorenstein dimension at most one. As an application, this result generalizes work by Koenig and Zhu.

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Yu Liu, Panyue Zhou. 2019-04-22. Gorenstein dimension of abelian categories. https://arxiv.org/abs/1904.09797

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