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From Right (n + 2)-angulated Categories to n-exangulated Categories

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Abstract

In this paper, we introduce the notion of a right semi-equivalence for right (n + 2)-angulated categories. Let \(\mathscr{C}\) be an n-exangulated category and \(\mathscr{X}\) be a strongly covariantly finite subcategory of \(\mathscr{C}\). We prove that the right (n + 2)-angulated category \(\mathscr{C}/\mathscr{X}\) has an n-suspension functor that is a right semi-equivalence under a natural assumption. As an application, we show that a right (n + 2)-angulated category has an n-exangulated structure if and only if the n-suspension functor is a right semi-equivalence. Furthermore, we also prove that an n-exangulated category \(\mathscr{C}\) has the structure of a right (n + 2)-angulated category with a right semi-equivalence if and only if for any object \(X \in \mathscr{C}\), the morphism X → 0 is a trivial inflation.

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Acknowledgements

Jian He is supported by the National Natural Science Foundation of China (No. 12171230) and Youth Science and Technology Foundation of Gansu Provincial (No. 23JRRA825). Jing He is supported by the Hunan Provincial Natural Science Foundation of China (No. 2023JJ40217). Panyue Zhou is supported by the National Natural Science Foundation of China (No. 12371034) and the Hunan Provincial Natural Science Foundation of China (No. 2023JJ30008).

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Authors and Affiliations

  1. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050, China

    Jian He

  2. School of Science, Hunan University of Technology and Business, Changsha, 410205, China

    Jing He

  3. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, China

    Panyue Zhou

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  1. Jian He
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  2. Jing He
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  3. Panyue Zhou
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Correspondence to Jing He.

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He, J., He, J. & Zhou, P. From Right (n + 2)-angulated Categories to n-exangulated Categories. Front. Math (2024). https://doi.org/10.1007/s11464-023-0121-y

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  • DOI: https://doi.org/10.1007/s11464-023-0121-y

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