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Higher Auslander-Reiten sequences revisited by He, Jian; Yin, Hangyu; Zhou, Panyue is a scholarly article available to read on EtoBox.

What is Higher Auslander-Reiten sequences revisited about?

Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an $n$-exangulated category with enough projectives and enough injectives, and $\mathscr{X}$ be a cluster-tilting subcategory of $\mathscr{C}$. Liu and Zhou have shown that the quotient category $\mathscr{C}/\mathscr{X}$ is an $n$-abelian category. In this paper, we prove that if $\mathscr{C}$ has Auslander-Reiten $n$-exangles, then $\mathscr{C}/\mathscr{X}$ has Auslander-Reiten $n$-exact sequences. Moreover, we also show that if a Frobenius $n$-exangulated category $\mathscr{C}$ has Auslander-Reiten $n$-exangles, then the stable category $\overline{\mathscr{C}}$ of $\mathscr{C}$ has Auslander-Reiten $(n+2)$-angles.

Author

He, Jian; Yin, Hangyu; Zhou, Panyue

Published

2024

Language

EN