WebMar 14, 2024 · Thirdly, we explore properties of silting subcategories of the subcategory consisting of objects with finite projective dimension. As an application, we can recover Auslander--Reiten's result which gives a bijection between tilting modules and contravariantly finite resolving subcategories with finite projective dimension. … WebIn this paper, we construct a recollement of abelian categories (mod0-X,mod-X,mod-A) ( m o d 0 - X, m o d - X, m o d - A), where mod0-X m o d 0 - X is a full subcategory of mod-X m o d - X consisting of all functors vanishing on projective modules.
Contravariantly finite resolving subcategories over commutative …
WebMar 7, 2024 · In this paper, by using functor rings and functor categories, we study finiteness and purity of subcategories of the module categories. We give a characterisation of contravariantly finite resolving subcategories of the module category of finite representation type in terms of their functor rings. WebMay 1, 2014 · Let Cbe a contravariantly finite subcategory of an abelian category A. One can define the C-relative derived category of A, denoted by DC⁎(A), similarly. Rickard provided a Morita theory for derived categories. We introduce and study relative Morita theory for Gorenstein derived categories. react render html from string
Recollements for dualizing 𝑘-varieties and Auslander’s formulas
WebApr 9, 2024 · Let C be a triangulated category with a Serre functor S and X a non-zero contravariantly finite rigid subcategory of C. Then X is cluster tilting if and only if the quotient category C/X is abelian and S (X)=X [2]. As an application, this result generalizes work by Beligiannis. Submission history From: Panyue Zhou [ view email ] WebCONTRAVARIANTLY FINITE RESOLVING SUBCATEGORIES 3 Corollary 1.5 (Christensen-Piepmeyer-Striuli-Takahashi). Suppose that there is a non-free totally reflexive R-module.If the full subcategory of modRconsisting of all totally reflexive R-modules is contravariantly finite, then Ris Gorenstein. A totally reflexive module was … WebJan 3, 2024 · We push this further by proposing an index with respect to a contravariantly finite, rigid subcategory, and we show this index behaves similarly to the classical index. Let \mathcal {C} be a skeletally small triangulated category with split idempotents, which is thus an extriangulated category (\mathcal {C},\mathbb {E},\mathfrak {s}). how to stay slim without exercise