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Keywords:
$(n+2)$-angulated category; cluster tilting subcategory; $n$-abelian category; Auslander-Reiten $(n+2)$-angle; Auslander-Reiten $n$-exact sequence
$(n+2)$-angulated category; cluster tilting subcategory; $n$-abelian category; Auslander-Reiten $(n+2)$-angle; Auslander-Reiten $n$-exact sequence
Summary:
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.
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