Relative quasi-Gorensteinness in extriangulated categories
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929673986899968 |
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| author | He, Zhenggang |
| author_facet | He, Zhenggang |
| contents | Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $ξ$ of $\mathbb{E}$-triangles. In this paper, we study the quasi-Gorensteinness of extriangulated categories. More precisely, we introduce the notion of quasi-$ξ$-projective and quasi-$ξ$-Gorenstein projective objects, investigate some of their properties and their behavior with respect to $\mathbb{E}$-triangles. Moreover, we give some equivalent characterizations of objects with finite quasi-$ξ$-Gorenstein projective dimension. As an application, our main results generalize Mashhad and Mohammadi's work in module categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative quasi-Gorensteinness in extriangulated categories He, Zhenggang Representation Theory Category Theory 18E05, 18G05, 18G20, 18G25 Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $ξ$ of $\mathbb{E}$-triangles. In this paper, we study the quasi-Gorensteinness of extriangulated categories. More precisely, we introduce the notion of quasi-$ξ$-projective and quasi-$ξ$-Gorenstein projective objects, investigate some of their properties and their behavior with respect to $\mathbb{E}$-triangles. Moreover, we give some equivalent characterizations of objects with finite quasi-$ξ$-Gorenstein projective dimension. As an application, our main results generalize Mashhad and Mohammadi's work in module categories. |
| title | Relative quasi-Gorensteinness in extriangulated categories |
| topic | Representation Theory Category Theory 18E05, 18G05, 18G20, 18G25 |
| url | https://arxiv.org/abs/2501.07140 |