- Turkish Journal of Mathematics
- Vol: 41 Issue: 1
- $\mathcal{W}$-Gorenstein objects in triangulated categories
$\mathcal{W}$-Gorenstein objects in triangulated categories
Authors : Chaoling Huang, Kaituo Liu
Pages : 138-157
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Publication Date : 9999-12-31
Article Type : Makaleler
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 $\xi xt^i_\xi(W,\ W')=0$ 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 $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object in $\mathcal{C}$ and study the properties of $\mathcal{W}$-Gorenstein objects and characterize the finite $\mathcal{G}(\mathcal{W})$-(co)resolution dimensions of any object. Some applications are given.Keywords : Triangulated category, proper class of triangles, $mathcal{W}$-Gorenstein object