Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2022; 59(1): 171-192

Online first article January 1, 2022      Printed January 1, 2022

https://doi.org/10.4134/JKMS.j210271

Copyright © The Korean Mathematical Society.

Grothendieck group for sequences

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 [1] 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 [4].

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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