Article
| Title: | Two results of $n$-exangulated categories (English) |
| Author: | He, Jian |
| Author: | He, Jing |
| Author: | Zhou, Panyue |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 177-189 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | M. Herschend, Y. Liu, H. Nakaoka introduced $n$-exangulated categories, which are a simultaneous generalization of $n$-exact categories and $(n+2)$-angulated categories. This paper consists of two results on $n$-exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an $n$-exangulated category. (English) |
| Keyword: | $n$-exangulated category |
| Keyword: | homotopy cartesian square |
| Keyword: | half exact functor |
| MSC: | 18E10 |
| MSC: | 18G80 |
| DOI: | 10.21136/CMJ.2023.0042-23 |
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| Date available: | 2024-03-13T10:06:52Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152274 |
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| Reference: | [1] Herschend, M., Liu, Y., Nakaoka, H.: $n$-exangulated categories (I): Definitions and fundamental properties.J. Algebra 570 (2021), 531-586. Zbl 1506.18015, MR 4188310, 10.1016/j.jalgebra.2020.11.017 |
| Reference: | [2] Herschend, M., Liu, Y., Nakaoka, H.: $n$-exangulated categories (II): Constructions from $n$-cluster tilting subcategories.J. Algebra 594 (2022), 636-684. Zbl 07459388, MR 4355116, 10.1016/j.jalgebra.2021.11.042 |
| Reference: | [3] Hu, J., Zhang, D., Zhou, P.: Two new classes of $n$-exangulated categories.J. Algebra 568 (2021), 1-21. Zbl 1458.18006, MR 4166049, 10.1016/j.jalgebra.2020.09.041 |
| Reference: | [4] Kong, X., Lin, Z., Wang, M.: The (ET4) axiom for extriangulated categories.Available at https://arxiv.org/abs/2112.06445 (2021), 13 pages. 10.48550/arXiv.2112.06445 |
| Reference: | [5] Liu, Y., Nakaoka, H.: Hearts of twin cotorsion pairs on extriangulated categories.J. Algebra 528 (2019), 96-149. Zbl 1419.18018, MR 3928292, 10.1016/j.jalgebra.2019.03.005 |
| Reference: | [6] Liu, Y., Zhou, P.: Frobenius $n$-exangulated categories.J. Algebra 559 (2020), 161-183. Zbl 1448.18022, MR 4096714, 10.1016/j.jalgebra.2020.03.036 |
| Reference: | [7] Nakaoka, H., Palu, Y.: Extriangulated categories, Hovey twin cotorsion pairs and model structures.Cah. Topol. Géom. Différ. Catég. 60 (2019), 117-193. Zbl 1451.18021, MR 3931945 |
| Reference: | [8] Ogawa, Y.: Auslander's defects over extriangulated categories: An application for the general heart construction.J. Math. Soc. Japan 73 (2021), 1063-1089. Zbl 1485.18010, MR 4329022, 10.2969/jmsj/84578457 |
| Reference: | [9] Sakai, A.: Relative extriangulated categories arising from half exact functors.J. Algebra 614 (2023), 592-610. Zbl 1499.18013, MR 4499356, 10.1016/j.jalgebra.2022.10.008 |
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