$\mathcal{W}$-Gorenstein objects in triangulated categories

Authors : Chaoling HUANG, Kaituo LIU

Pages : 138-157

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We fix a proper class of triangles $\xi$ in a triangulated category $\mathcal{C}$. Let $\mathcal{W}$ be a class of objects in $\mathcal{C}$ such that $\xi xt^i_\xiinsert ignore into journalissuearticles values(W,\ W`);=0$ for all $W, W`\in\mathcal{W}$ and all $i\geq 1$. In this paper, we introduce the notion of $\mathcal{W}$-Gorenstein objects and $\mathcal{G}insert ignore into journalissuearticles values(\mathcal{W});$-insert ignore into journalissuearticles values(co);resolution dimensions of any object in $\mathcal{C}$ and study the properties of $\mathcal{W}$-Gorenstein objects and characterize the finite $\mathcal{G}insert ignore into journalissuearticles values(\mathcal{W});$-insert ignore into journalissuearticles values(co);resolution dimensions of any object. Some applications are given.
Keywords : Triangulated category, proper class of triangles, mathcal W Gorenstein object