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arXiv · 2006.02223

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

Yu Liu·Panyue Zhou
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Abstract

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.

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BibTeXRIS

Yu Liu, Panyue Zhou. 2020-06-02. From $n$-exangulated categories to $n$-abelian categories. https://arxiv.org/abs/2006.02223

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