The Grothendieck Group of an $n$-exangulated Category

Autor:	Haugland, Johanne
Rok vydání:	2019
Předmět:	Mathematics - Category Theory Mathematics - K-Theory and Homology Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: 18 pages. Final version, accepted for publication in Applied Categorical Structures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1912.04328 Zobrazit plný text záznamu View this record from Arxiv