$n$-abelian quotient categories

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