2024/05/01 by Erlend D. Børve, Børve, Erlend D.
Chemical Engineering · Medicine · Mathematics · #Catalysis and Oxidation Reactions #Intracranial Aneurysms: Treatment and Complications #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2405.00593
Let C be an extriangulated category and let R⊆ C be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a technical condition (gCP) on R which is sufficient for the Verdier quotient C/thick(R) to be equivalent to an ideal quotient. In particular, the Verdier quotient C/thick(R) will admit an extriangulation in such a way that the localization functor LR\colon C → C/thick(R) is extriangulated. When C is 0-Auslander, the condition (gCP) holds for all rigid subcategories R admitting Bongartz completions. Furthermore, we prove that the Verdier quotient C/thick(R) then remains 0-Auslander. As an application, we define the picture category of a connective 0-Auslander exact dg category \mathscrA with Bongartz completions, which generalizes the notion of τ-cluster morphism category. We show that the picture category of \mathscrA is a cubical category, in the sense of Igusa. The picture group of \mathscrA is defined as the fundamental group of its picture category. When H0\mathscrA is g-finite, the picture group of \mathscrA is finitely presented.