The axioms for n-angulated categories

Abstract

We discuss the axioms for an n-angulated category, recently introduced by Geiss, Keller and Oppermann. In particular, we introduce a higher octahedral axiom, and show that it is equivalent to the mapping cone axiom for an n-angulated category. For a triangulated category, the mapping cone axiom, our octahedral axiom and the classical octahedral axiom are all equivalent.

17 pages, added a section, updated references

References in corpus (1)

• $n$-angulated categories

Cited by in corpus (22)

• $n$-abelian and $n$-exact categories
• $n$-exangulated categories
• Maximal ${\tau }_d$-rigid pairs
• Higher n-angulations from local rings
• The morphism axiom for n-angulated categories
• Right $n$-angulated categories arising from covariantly finite subcategories
• $n$-Exact categories arising from $(n+2)$-angulated categories
• Higher gentle algebras
• Homotopy cartesian diagrams in n-angulated categories
• Frobenius $n$-exangulated categories
• N-extension closed subcategories of (n+2)-angulated categories
• n-angulated quotient categories induced by mutation pairs
• The bivariant parasimplicial ${\mathsf{S}}_{\bullet }$-construction
• $n$-abelian quotient categories
• $n$-angulated categories from self-injective algebras
• A general construction of $n$-angulated categories using periodic injective resolutions
• A new characterization of n-exangulated categories with (n+2)-angulated structure
• Ideal approximation in $n$-angulated categories
• From right (n+2)-angulated categories to n-exangulated categories
• Two new classes of n-exangulated categories
• From $n$-exangulated categories to $n$-abelian categories
• Grothendieck groups and Auslander-Reiten (d+2)-angles