Higher-dimensional Auslander-Reiten sequences

Zhou and Zhu have shown that if C is an ( n + 2)-angulated category and X is a cluster tilting subcategory of C , then the quotient category C / X is an n -abelian category. We show that if C has Auslander-Reiten ( n + 2)-angles, then C / X has Auslander-Reiten n -exact sequences.

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Veröffentlicht in:	Czechoslovak Mathematical Journal 2024, Vol.74 (3), p.771-786
Hauptverfasser:	Li, Jiangsha, He, Jing
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Convex and Discrete Geometry Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Ordinary Differential Equations
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Beschreibung
Zusammenfassung:	Zhou and Zhu have shown that if C is an ( n + 2)-angulated category and X is a cluster tilting subcategory of C , then the quotient category C / X is an n -abelian category. We show that if C has Auslander-Reiten ( n + 2)-angles, then C / X has Auslander-Reiten n -exact sequences.
ISSN:	0011-4642 1572-9141
DOI:	10.21136/CMJ.2024.0545-23