Silting reduction in extriangulated categories

Yu Liu, Panyue Zhou, Yu Zhou, Bin Zhu

Published 2021-08-18Version 1

We introduce pre-silting and silting subcategories in extriangulated categories and generalize the silting theory in triangulated categories. We prove that the silting reduction $\mathcal B/({\rm thick}\mathcal W)$ of an extriangulated category $\mathcal B$ with respect to a pre-silting subcategory $\mathcal W$ can be realized as a certain subfactor category of $\mathcal B$. This generalizes the result by Iyama-Yang. In particular, for a Gorenstein algebra, we get the relative version of the description of the singularity category due to Happel and Chen-Zhang by this reduction.