Generalized Gorenstein Categories
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912961067483136 |
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| author | Huang, Zhaoyong |
| author_facet | Huang, Zhaoyong |
| contents | Let $\mathscr{A}$ be an abelian category and let $\mathscr{C}$ and $\mathscr{D}$ be additive subcategories of $\mathscr{A}$. As a generalization of Gorenstein categories, we introduce one-sided $n$-$(\C,\D)$-Gorenstein categories with $n\geq 0$. Under certain conditions, we give some equivalent characterizations of one-sided $n$-$(\C,\D)$-Gorenstein categories in term of the finiteness of projective and injective dimensions relative to one-sided Gorenstein subcategories, which induce some new equivalent characterizations of Gorenstein categories. Then we apply these results to categories of interest. In particular, a necessary condition is obtained for the validity of the Wakamatsu tilting conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04856 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Gorenstein Categories Huang, Zhaoyong Category Theory Rings and Algebras 18G25, 16E10 Let $\mathscr{A}$ be an abelian category and let $\mathscr{C}$ and $\mathscr{D}$ be additive subcategories of $\mathscr{A}$. As a generalization of Gorenstein categories, we introduce one-sided $n$-$(\C,\D)$-Gorenstein categories with $n\geq 0$. Under certain conditions, we give some equivalent characterizations of one-sided $n$-$(\C,\D)$-Gorenstein categories in term of the finiteness of projective and injective dimensions relative to one-sided Gorenstein subcategories, which induce some new equivalent characterizations of Gorenstein categories. Then we apply these results to categories of interest. In particular, a necessary condition is obtained for the validity of the Wakamatsu tilting conjecture. |
| title | Generalized Gorenstein Categories |
| topic | Category Theory Rings and Algebras 18G25, 16E10 |
| url | https://arxiv.org/abs/2603.04856 |