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n-extension closed subcategories of \((n+2)\)-angulated categories

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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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References

  1. Bergh, P., Thaule, M.: The axioms for \(n\)-angulated categories. Algebr. Geom. Topol. 13(4), 2405–2428 (2013)

    Article  MathSciNet  Google Scholar 

  2. Dyer, M.J.: Exact subcategories of triangulated categories. Preprint (2005). https://www3.nd.edu/~dyer/papers/extri.pdf

  3. Geiss, C., Keller, B., Oppermann, S.: \(n\)-angulated categories. J. Reine Angew. Math. 675, 101–120 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Herschend, M., Liu, Y., Nakaoka, H.: \(n\)-exangulated categories (I): Definitions and fundamental properties. J. Algebra 570, 531–586 (2021)

    Article  MathSciNet  Google Scholar 

  5. Hu, J., Zhang, D., Zhou, P.: Two new classes of \(n\)-exangulated categories. J. Algebra 568, 1–21 (2021)

    Article  MathSciNet  Google Scholar 

  6. Jasso, G.: \(n\)-abelian and \(n\)-exact categories. Math. Z 283(3–4), 703–759 (2016)

    Article  MathSciNet  Google Scholar 

  7. Jørgensen, P.: Abelian subcategories of triangulated categories induced by simple minded systems. arXiv: 2010.11799 (2021)

  8. Klapproth, C.: \(n\)-exact categories arising from \((n+2)\)-angulated categories. arXiv: 2108.04596 (2021)

  9. Lin, Z.: \(n\)-angulated quotient categories induced by mutation pairs. Czechoslovak Math. J. 65(140)(4), 953–968 (2015)

    Article  MathSciNet  Google Scholar 

  10. Lin, Z.: Idempotent completion of \(n\)-angulated categories. Appl. Categ. Struct. 29(6), 1063–1071 (2021)

    Article  MathSciNet  Google Scholar 

  11. Liu, Y., Zhou, P.: Frobenius \(n\)-exangulated categories. J. Algebra 559, 161–183 (2020)

    Article  MathSciNet  Google Scholar 

  12. Nakaoka, H., Palu, Y.: Extriangulated categories, Hovey twin cotorsion pairs and model structures. Cah. Topol. Géom. Différ. Catég. 60(2), 117–193 (2019)

    MathSciNet  MATH  Google Scholar 

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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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  1. College of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, Hunan, People’s Republic of China

    Panyue Zhou

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  1. Panyue Zhou
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Correspondence to Panyue Zhou.

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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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