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Contravariantly finite

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 https://carlsonhamer.com

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

Applications of contravariantly finite subcategories - ScienceDirect

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Contravariantly finite

(PDF) Finite Projectivity and Contravariant Finiteness

http://users.uoi.gr/abeligia/gorenstein.pdf WebJun 20, 2024 · Model categories structures from rigid objects in exact categories. Lucie Jacquet-Malo. Let be a weakly idempotent complete exact category with enough injective and projective objects. Assume that is a rigid, contravariantly finite subcategory of containing all the injective and projective objects, and stable under taking direct sums …

Contravariantly finite

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WebABSTRACT We define right n-angulated categories, which are analogous to right triangulated categories. Let 𝒞 be an additive category and 𝒳 a covariantly finite … WebApr 1, 1990 · Let A be the algebra given by the quiver 1 It is shown in [9] that these maps do not factor through an A-module of finite projective dimension, proving that P <∞ is not contravariantly finite ...

Webusers.uoi.gr - University of Ioannina WebIt is well-known that contravariantly finite subcategories enjoy various basic properties of the classical one (i.e. Proj R) and the subcategory GPR. Based on these results, two …

WebJun 27, 2007 · Let modA be the category of finitely generated right A-modules over an artin algebra ⋀, and F be an additive subfunctor of . Let P(F) denote the full sucategory of A with objects the F-projective... WebIn summary, for covariant functors, the unlifted and lifted functions point in the same direction, z0 -> z1. With contravariance, the unlifted and lifted functions point in opposite …

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 …

WebJan 27, 2024 · the subcategory \({\mathcal {X}}\) is contravariantly finite and \({\mathcal {Y}}\) is covariantly finite; (BP2) for each object M , there is an \({\mathcal {X}}\) -resolution \(X^{\bullet }\rightarrow M\) such that it is \(\text {Hom}_{{\mathscr {A}}}(-,{\mathcal {Y}})\) … react render ifWebFeb 1, 2024 · The reverse implication, namely P ∞ fin is contravariantly finite ⇒ GP ∞ fin is contravariantly finite, it proved in Theorem (2.5) for Artin algebras over which the class GP 0 fin is contravariantly finite. Typical examples of such Artin algebras are CM-finite and virtually Gorenstein Artin algebras; cf. Remark (2.6). react render html string from serverWebJun 27, 2007 · Let P (F) denote the full sucategory of A with objects the F -projective modules. If the functor F has enough F - projectives, then we show that the stable … how to stay small and weakWebJan 26, 2024 · The homological theory of contravariantly finite subcategories: Auslander-Buchweitz contexts, Gorenstein categories and (co)stabilization. Comm. Algebra 28 ( 2000 ), 4547 – 4596. CrossRef Google Scholar 6 Bergh, P. A., Jørgensen, D. A. and Oppermann, S.. The Gorenstein defect category. Q. J. Math. 66 ( 2015 ), 459 – 471. CrossRef Google … how to stay sober on vacationWebIt admits a homological interpretation and enjoys a reciprocity smon ( Q, I, ⊥ T) = ⊥ ( T ⊗ k Q / I) for a cotilting A -module T. As an application, smon ( Q, I, X) has Auslander-Reiten sequences if X is resolving and contravariantly finite with X ^ = 𝐴-mod . In particular, smon ( Q, I, A) has Auslander-Reiten sequences. react render nbspWebIf R is an artin algebra, then T can be taken to be finitely generated iff P < ∞ is contravariantly finite. We also obtain a sufficient condition for validity of the First Finitistic Dimension Conjecture that extends the well-known result of Huisgen-Zimmermann and Smalø. (Show Context) MODULES WITH COSUPPORT AND INJECTIVE FUNCTORS ... react render json objectWebOct 6, 2024 · The objective of this paper is to study the relative homological properties of contravariantly and covariantly finite subcategories. Some sufficient conditions for E x t ¯ Y n A , B ≃ E x t ¯ X... how to stay still during an mri