Abstract
Let $\mathcal {T}$ be a triangulated category with triangulation $\Delta $, $\xi \subseteq \Delta $ a proper class of triangles and $\mathcal {C}$ an additive full subcategory of $\mathcal {T}$. We provide a method for constructing a proper $\mathcal {C}(\xi )$-resolution (respectively, coproper $\mathcal {C}(\xi )$-coresolution) of one term in a triangle in $\xi $ from those of the other two terms. By using this construction, we show the stability of the Gorenstein category $\mathcal {GC}(\xi )$ in triangulated categories. Some applications are given.
Citation
Xiaoyan Yang. Zhicheng Wang. "Proper resolutions and Gorensteinness in triangulated categories." Rocky Mountain J. Math. 47 (3) 1013 - 1053, 2017. https://doi.org/10.1216/RMJ-2017-47-3-1013
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