$n$-abelian quotient categories

Abstract

Let $\C$ be an $(n+2)$-angulated category with shift functor $\Sigma$ and $\X$ be a cluster-tilting subcategory of $\C$. Then we show that the quotient category $\C/\X$ is an $n$-abelian category. If $\C$ has a Serre functor, then $\C/\X$ is equivalent to an $n$-cluster tilting subcategory of an abelian category $\textrm{mod}(Σ^{-1}\X)$. Moreover, we also prove that $\textrm{mod}(Σ^{-1}\X)$ is Gorenstein of Gorenstein dimension at most $n$. As an application, we generalize recent results of Jacobsen-Jørgensen and Koenig-Zhu.

14 pages

References in corpus (3)

• $d$-abelian quotients of $(d+2)$-angulated categories
• Projectively generated $d$-abelian categories are $d$-cluster tilting
• The triangulation of the subfactor categories of additive categories with suspensions