Abstract
Let \({\mathscr {C}}\) be a Krull-Schmidt \((n+2)\)-angulated category and \({\mathscr {A}}\) be an n-extension closed subcategory of \({\mathscr {C}}\). Then \({\mathscr {A}}\) has the structure of an n-exangulated category in the sense of Herschend–Liu–Nakaoka. This construction gives n-exangulated categories which are not n-exact categories in the sense of Jasso nor \((n+2)\)-angulated categories in the sense of Geiss–Keller–Oppermann in general. As an application, our result can lead to a recent main result of Klapproth
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Acknowledgements
The author would like to thank Yonggang Hu and Tiwei Zhao for the helpful discussions. The author would also like to thank the referee for reading the paper carefully and for many suggestions on mathematics and English expressions.
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This work was supported by the National Natural Science Foundation of China (Grant No. 11901190) and the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 19B239)
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Zhou, P. n-extension closed subcategories of \((n+2)\)-angulated categories. Arch. Math. 118, 375–382 (2022). https://doi.org/10.1007/s00013-022-01705-5
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DOI: https://doi.org/10.1007/s00013-022-01705-5
Keywords
- \((n+2)\)-angulated categories
- n-exact categories
- n-extension closed subcategories
- n-exangulated categories