2019/12/09 by Haugland, Johanne
#Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1912.04328
We define the Grothendieck group of an n-exangulated category. For n odd, we show that this group shares many properties with the Grothendieck group of an exact or a triangulated category. In particular, we classify dense complete subcategories of an n-exangulated category with an n-(co)generator in terms of subgroups of the Grothendieck group. This unifies and extends results of Thomason, Bergh--Thaule, Matsui and Zhu--Zhuang for triangulated, (n+2)-angulated, exact and extriangulated categories, respectively. We also introduce the notion of an n-exangulated subcategory and prove that the subcategories in our classification theorem carry this structure.