Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GROTHENDIECK GROUP FOR SEQUENCES

  • Yu, Xuan (Public Course Education Department Shenzhen Institute of Information Technology)
  • Received : 2021.04.23
  • Accepted : 2021.09.24
  • Published : 2022.01.01
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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

Acknowledgement

The author would like to thank the reviewer for the helpful suggestions in improving the content of the paper. 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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