2012/05/25 by Petter Andreas Bergh, Bergh, Petter Andreas, Marius Thaule +1
Mathematics · #18E30 #18F30 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1205.5697
openalex publication_date 2012/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n=3, i.e. the triangulated case. In particular, its subgroups classify the dense and complete n-angulated subcategories via a bijective correspondence. For a tensor n-angulated category, the Grothendieck group becomes a ring, whose ideals classify the dense and complete n-angulated tensor ideals of the category.