$n$-exangulated categories

Abstract

For each positive integer $n$ we introduce the notion of $n$-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. We characterize which $n$-exangulated categories are $n$-exact in the sense of Jasso and which are $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann. For extriangulated categories with enough projectives and injectives we introduce the notion of $n$-cluster tilting subcategories and show that under certain conditions such $n$-cluster tilting subcategories are $n$-exangulated.

Section 6 added. 71 pages

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• Higher Nakayama algebras I: Construction
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• Tensor products of n-complete algebras
• Gluing of $n$-cluster tilting subcategories for representation-directed algebras
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Cited by in corpus (14)

• Associahedra for finite type cluster algebras and minimal relations between $\mathbf{g}$-vectors
• Classifying substructures of extriangulated categories via Serre subcategories
• External triangulation of the homotopy category of exact quasi-category
• On the lattices of exact and weakly exact structures
• Positive and negative extensions in extriangulated categories
• Grothendieck groups in extriangulated categories
• Frobenius $n$-exangulated categories
• Idempotent completion of extriangulated categories
• Right triangulated categories: As extriangulated categories, aisles and co-aisles
• Higher Auslander's defect and classifying substructures of n-exangulated categories
• From $n$-exangulated categories to $n$-abelian categories
• Two new classes of n-exangulated categories
• A new characterization of n-exangulated categories with (n+2)-angulated structure
• Grothendieck groups and Auslander-Reiten (d+2)-angles