The Grothendieck group of an n-angulated category

TL;DR

This paper introduces the Grothendieck group for n-angulated categories, extending known properties from the triangulated case and establishing a classification of subcategories and tensor ideals.

Contribution

It defines the Grothendieck group for n-angulated categories and explores its properties, generalizing results from the triangulated case to odd n.

Findings

Grothendieck group classification of subcategories

Ring structure for tensor n-angulated categories

Bijective correspondence between subgroups and subcategories

Abstract

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.