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Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. Itis not only a higher dimensional analogue of extriangulated categories definedby Nakaoka-Palu, but also gives a simultaneous generalization of $n$-exactcategories in the sense of Jasso and $(n+2)$-angulated in the sense ofGeiss-Keller-Oppermann. Let $\mathscr C$ be an $n$-exangulated category withenough projectives and enough injectives, and $\mathscr X$ a cluster tiltingsubcategory of $\mathscr C$. In this article, we show that the quotientcategory $\mathscr C/\mathscr X$ is an $n$-abelian category. This extends aresult of Zhou-Zhu for $(n+2)$-angulated categories. Moreover, it highlightsnew phenomena when it is applied to $n$-exact categories.

From $n$-exangulated categories to $n$-abelian categories