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arXiv · 2603.04856

Generalized Gorenstein Categories

Zhaoyong Huang
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Abstract

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.

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Zhaoyong Huang. 2026-03-05. Generalized Gorenstein Categories. https://arxiv.org/abs/2603.04856

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