n-Abelian quotient categories

Add time:08/01/2019    Source:sciencedirect.com

Let C be an (n+2)-angulated category with an n-suspension functor Σn and X be a cluster-tilting subcategory of C. Then we show that the quotient category C/X is an n-abelian category, and C/X is equivalent to an n-cluster tilting subcategory of an abelian category mod(Σ−nX). In addition, if C has a Serre functor, we also prove that mod(Σ−nX) is Gorenstein of Gorenstein dimension at most n. As an application, we generalize recent results of Jacobsen-Jørgensen and Koenig-Zhu.

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