Silting reduction in extriangulated categories

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 $\mathcal{B}/(\mathrm{thick}\mathcal{W})$ 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.

22 pages

References in corpus (1)

• External triangulation of the homotopy category of exact quasi-category