Abstract
Let \({\cal C}\) be a Krull–Schmidt n-exangulated category and \({\cal A}\) be an n-extension closed subcategory of \({\cal C}\). Then \({\cal A}\) inherits the n-exangulated structure from the given n-exangulated category in a natural way. This construction gives n-exangulated categories which are neither n-exact categories in the sense of Jasso nor (n + 2)-angulated categories in the sense of Geiss–Keller–Oppermann in general. Furthermore, we also give a sufficient condition on when an n-exangulated category \({\cal A}\) is an n-exact category. These results generalize work by Klapproth and Zhou.
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Acknowledgements
The authors would like to thank the referee for reading the paper carefully and for many suggestions on mathematics and English expressions.
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J. He was supported by the National Natural Science Foundation of China (Grant No. 12171230), P. Zhou was supported by the Hunan Provincial Natural Science Foundation of China (Grant No. 2023JJ30008)
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He, J., Zhou, P.Y. n-exact Categories Arising from n-exangulated Categories. Acta. Math. Sin.-English Ser. 39, 1781–1794 (2023). https://doi.org/10.1007/s10114-023-1558-3
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DOI: https://doi.org/10.1007/s10114-023-1558-3
Keywords
- (n + 2)-angulated categories
- n-exact categories
- n-extension closed subcategories
- n-exangulated categories