Silting reduction and picture categories of 0-Auslander extriangulated categories

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 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 A with Bongartz completions, which generalizes the notion of τ-cluster morphism category. We show that the picture category of A is a cubical category, in the sense of Igusa. The picture group of A is defined as the fundamental group of its picture category. When H₀A is g-finite, the picture group of A is finitely presented.