| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| idZBL:
|
Zbl 07893373 |
| idMR:
|
MR4717828 |
| DOI:
|
10.21136/CMJ.2023.0042-23 |
| . |
| Date available:
|
2024-03-13T10:06:52Z |
| Last updated:
|
2026-04-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152274 |
| . |
| 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 |
| . |
