题目：Generalized Gorenstein categories

报告人：黄兆泳 教授，南京大学

时间：2025年11月21日下午，16:00-17:00

地点：第五教学楼5306

摘要：Let $\mathscr{A}$ be an abelian category and let $\mathscr{C}$ and $\mathscr{D}$ be subcategories of $\mathscr{A}$. As a generalization of Gorenstein categories, we introduce one-sided $n$-$(\mathscr{C},\mathscr{D})$-Gorenstein categories with $n\geq 0$. Under certain conditions, we give some equivalent characterizations of one-sided $n$-$(\mathscr{C},\mathscr{D})$-Gorenstein categoriesin 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.