2021/08/18 by Yu Liu, Panyue Zhou, Liu, Yu +5
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2108.07964
openalex publication_date 2021/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.