  Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It
is not only a higher dimensional analogue of extriangulated categories defined
by Nakaoka-Palu, but also gives a simultaneous generalization of $n$-exact
categories in the sense of Jasso and $(n+2)$-angulated in the sense of
Geiss-Keller-Oppermann. Let $\mathscr C$ be an $n$-exangulated category with
enough projectives and enough injectives, and $\mathscr X$ a cluster tilting
subcategory of $\mathscr C$. In this article, we show that the quotient
category $\mathscr C/\mathscr X$ is an $n$-abelian category. This extends a
result of Zhou-Zhu for $(n+2)$-angulated categories. Moreover, it highlights
new phenomena when it is applied to $n$-exact categories.
