Article
| Title: | One-sided $n$-suspended categories (English) |
| Author: | He, Jing |
| Author: | Hu, Yonggang |
| Author: | Zhou, Panyue |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 1007-1039 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | For an integer $n\geq 3$, we introduce a simultaneous generalization of $(n-2)$-exact categories and $n$-angulated categories, referred to as one-sided $n$-suspended categories. Notably, one-sided $n$-angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their $n$-angulated counterparts. Additionally, we present a method for constructing $n$-angulated quotient categories from Frobenius $n$-prile categories. Our results unify and extend the previous work of Jasso on $n$-exact categories, Lin on $(n+2)$-angulated categories, and Li on one-sided suspended categories. (English) |
| Keyword: | triangulated category |
| Keyword: | $n$-angulated category |
| Keyword: | exact category |
| Keyword: | $(n-2)$-exact category |
| Keyword: | right $n$-angulated category |
| Keyword: | one-sided $n$-suspended category |
| MSC: | 18E10 |
| MSC: | 18G80 |
| DOI: | 10.21136/CMJ.2024.0424-23 |
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| Date available: | 2024-12-15T06:34:34Z |
| Last updated: | 2024-12-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152687 |
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| Reference: | [1] Bergh, P. A., Thaule, M.: The axioms for $n$-angulated categories.Algebr. Geom. Topol. 13 (2013), 2405-2428. Zbl 1272.18008, MR 3073923, 10.2140/agt.2013.13.2405 |
| Reference: | [2] Geiss, C., Keller, B., Oppermann, S.: $n$-angulated categories.J. Reine Angew. Math. 675 (2013), 101-120. Zbl 1271.18013, MR 3021448, 10.1515/CRELLE.2011.177 |
| Reference: | [3] Jasso, G.: $n$-abelian and $n$-exact categories.Math. Z. 283 (2016), 703-759. Zbl 1356.18005, MR 3519980, 10.1007/s00209-016-1619-8 |
| Reference: | [4] Li, Z.-W.: Homotopy theory in additive categories with suspensions.Commun. Algebra 49 (2021), 5137-5170. Zbl 1484.18023, MR 4328528, 10.1080/00927872.2021.1938102 |
| Reference: | [5] Lin, Z.: $n$-angulated quotient categories induced by mutation pairs.Czech. Math. J. 65 (2015), 953-968. Zbl 1363.18009, MR 3441328, 10.1007/s10587-015-0220-3 |
| Reference: | [6] Lin, Z.: Right $n$-angulated categories arising from covariantly finite subcategories.Commun. Algebra 45 (2017), 828-840. Zbl 1371.18010, MR 3562541, 10.1080/00927872.2016.1175591 |
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