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

Authors

CHAOLING HUANG
KAITUO LIU

DOI

10.3906/mat-1507-61

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

First Page

138

Last Page

157

Recommended Citation

HUANG, CHAOLING and LIU, KAITUO (2017) "$\mathcal{W}$-Gorenstein objects in triangulated categories," Turkish Journal of Mathematics: Vol. 41: No. 1, Article 14. https://doi.org/10.3906/mat-1507-61
Available at: https://journals.tubitak.gov.tr/math/vol41/iss1/14