The axioms for right (n+2)-angulated categories
Jing He, Jiangsha Li
TL;DR
This paper refines the axioms for right (n+2)-angulated categories, demonstrating the redundancy of the morphism axiom and establishing the equivalence between the higher octahedral and mapping cone axioms.
Contribution
It introduces refined axioms for right (n+2)-angulated categories, showing the redundancy of the morphism axiom and the equivalence of key axioms.
Findings
Morphism axiom is redundant in right (n+2)-angulated categories
Higher octahedral axiom is equivalent to the mapping cone axiom
Provides examples of such categories
Abstract
Drawing inspiration from the works of Beligiannis-Marmaridis and Lin, we refine the axioms for a right -angulated category and give some examples of such categories. Interestingly, we show that the morphism axiom for a right -angulated category is actually redundant. Moreover, we prove that the higher octahedral axiom is equivalent to the mapping cone axiom for a right -angulated category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras