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Higher-dimensional Auslander-Reiten sequences
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 771-786
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Zhou and Zhu have shown that if $\mathscr {C}$ is an $(n+2)$-angulated category and $\mathscr {X}$ is a cluster tilting subcategory of $\mathscr{C}$, then the quotient category $\mathscr {C}/\mathscr {X}$ is an $n$-abelian category. We show that if $\mathscr {C}$ has Auslander-Reiten $(n+2)$-angles, then $\mathscr {C}/\mathscr {X}$ has Auslander-Reiten $n$-exact sequences.
Zhou and Zhu have shown that if $\mathscr {C}$ is an $(n+2)$-angulated category and $\mathscr {X}$ is a cluster tilting subcategory of $\mathscr{C}$, then the quotient category $\mathscr {C}/\mathscr {X}$ is an $n$-abelian category. We show that if $\mathscr {C}$ has Auslander-Reiten $(n+2)$-angles, then $\mathscr {C}/\mathscr {X}$ has Auslander-Reiten $n$-exact sequences.
DOI : 10.21136/CMJ.2024.0545-23
Classification : 16G70, 18E10, 18G80
Keywords: $(n+2)$-angulated category; cluster tilting subcategory; $n$-abelian category; Auslander-Reiten $(n+2)$-angle; Auslander-Reiten $n$-exact sequence 
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Li, Jiangsha; He, Jing. Higher-dimensional Auslander-Reiten sequences. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 771-786. doi: 10.21136/CMJ.2024.0545-23

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