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\(n\)-angulated quotient categories induced by mutation pairs. (English) Zbl 1363.18009

Summary: C. Geiss et al. [J. Reine Angew. Math. 675, 101–120 (2013; Zbl 1271.18013)] introduced the notion of \(n\)-angulated category, which is a “higher dimensional” analogue of triangulated category, and showed that certain \((n-2)\)-cluster tilting subcategories of triangulated categories give rise to \(n\)-angulated categories. We define mutation pairs in \(n\)-angulated categories and prove that given such a mutation pair, the corresponding quotient category carries a natural \(n\)-angulated structure. This result generalizes a theorem of O. Iyama and Y. Yoshino [Invent. Math. 172, No. 1, 117–168 (2008; Zbl 1140.18007)] for triangulated categories.

MSC:

18E30 Derived categories, triangulated categories (MSC2010)
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References:

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