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arXiv · 2108.07964

Silting reduction in extriangulated categories

Yu Liu·Panyue Zhou·Yu Zhou·Bin Zhu
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Abstract

Presilting and silting subcategories in extriangulated categories were introduced by Adachi and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization $\mathcal B/({\rm thick}\mathcal W)$ of an extriangulated category $\mathcal B$ with respect to a presilting subcategory $\mathcal W$ satisfying certain condition can be realized as a subfactor category of $\mathcal B$. This generalizes the result by Iyama-Yang for silting reduction on triangulated categories. Then we discuss the relation between silting subcategories and tilting subcategories in extriangulated categories, this gives us a kind of important examples of our results. In particular, for a finite dimensional Gorenstein algebra, we get the relative version of the description of the singularity category due to Happel and Chen-Zhang by this reduction.

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Yu Liu, Panyue Zhou, Yu Zhou, Bin Zhu. 2021-08-18. Silting reduction in extriangulated categories. https://arxiv.org/abs/2108.07964

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