The Grothendieck Group of an $n$-exangulated Category

Johanne Haugland

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arXiv · 1912.04328

The Grothendieck Group of an $n$-exangulated Category

Johanne Haugland

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Abstract

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.

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BibTeX RIS

Johanne Haugland. 2019-12-09. The Grothendieck Group of an $n$-exangulated Category. https://arxiv.org/abs/1912.04328

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