Grothendieck group for sequences
J. Korean Math. Soc. 2022 Vol. 59, No. 1, 171-192
Published online December 6, 2021
Printed January 1, 2022
Xuan Yu
Shenzhen Institute of Information Technology
Abstract : 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 Bergh-Thaule for $n$-angulated categories \cite{bergh2014grothendieck} are proven. A classification result of dense complete subcategories is given and we give a formal definition of K-groups for these categories following Grayson's algebraic approach of K-theory for exact categories \cite{grayson2012algebraic}.
Keywords : Grothendieck group, K-group, $n$-sequence
MSC numbers : 18F30, 18E30, 18E10
Supported by : This project was partially supported by the National Natural Science Foundation of China (Grant No. 11901589), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2018A030313581) and Shenzhen Institute of Information Technology (Grant No. SZIIT2021KJ022).
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