Grothendieck group for sequences. (English) Zbl 1481.18016

Yu, Xuan

J. Korean Math. Soc. 59, No. 1, 171-192 (2022).

Summary: For any category with a distinguished collection of sequences, such as \(n\)-exangulated category, category of \(N\)-complexes and category of precomplexes, we consider its Grothendieck group and similar results of P. A. Bergh and M. Thaule for \(n\)-angulated categories [J. Pure Appl. Algebra 218, No. 2, 354–366 (2014; Zbl 1291.18015)] are proven. A classification result of dense complete subcategories is given and we give a formal definition of \(K\)-groups for these categories following D. R. Grayson’s algebraic approach of \(K\)-theory for exact categories [J. Am. Math. Soc. 25, No. 4, 1149–1167 (2012; Zbl 1276.19003)].

MSC:

18F30	Grothendieck groups (category-theoretic aspects)
18G80	Derived categories, triangulated categories
18E10	Abelian categories, Grothendieck categories
19A99	Grothendieck groups and \(K_0\)
19D99	Higher algebraic \(K\)-theory

Keywords:

Grothendieck group; \(K\)-group; \(n\)-sequence

Citations:

Zbl 1291.18015; Zbl 1276.19003

References:

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[12]	Xuan Yu Public Course Education Department Shenzhen Institute of Information Technology Shenzhen 518172, P. R. China Email address: [e-mail]