Contravariantly finite
WebIf 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 ... WebBeligiannis, A. (2000). The homological theory of contravariantly finite subcategories:auslander-buchweitz contexts, gorenstein categories and (co-)stabilization.
Contravariantly finite
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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. http://users.uoi.gr/abeligia/gorenstein.pdf
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 … WebSep 10, 2014 · ABSTRACT We define right n-angulated categories, which are analogous to right triangulated categories. Let 𝒞 be an additive category and 𝒳 a covariantly finite subcategory of 𝒞. We show that under certain conditions, the quotient 𝒞∕ [𝒳] is a right n-angulated category. This has immediate applications to n-angulated quotient categories.
WebJan 1, 2001 · Abstract. Let (F, G) be an adjoint pair from a category A to a category B. The contravariantly finiteness of subcategories is proved to be preserved by F, and the … WebThe notion of a contravariantly finite subcategory (of the category of finitely generated modules), which is also called a (pre)covering class, was first introduced over artin algebras by Auslander and Smalø [] in connection with studying the problem of which subcategories admit almost split sequences. The notion of a resolving subcategory was introduced by …
WebDec 1, 2024 · It follows that T ⊥ > 0 is specially contravariantly finite in D +. Proposition 2.16. Assume that T ⊆ D ⩾ 0 is specially contravariantly finite in D + and is cosuspended such that T ˆ = D +. If T ⋂ T ⊥ > 0 is closed under products, then there is a cosilting complex T such that T = T ⊥ > 0. Proof. It is not difficult to verify that ...
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. nehemiah lesson for kidsitis archimede cammarataWebGiven the pair of a dualizing -variety and its functorially finite subcategory, we show that there exists a recollement consisting of their functor categories of finitely presented objects. We provide several applicati… nehemiah leadership styleWebMar 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. … nehemiah manufacturing cincinnatiWebLet ΛΛ\Lambdaroman_Λ be an artin algebra. We denote by mod ΛΛ\Lambdaroman_Λ the category of all finitely generated right ΛΛ\Lambdaroman_Λ-modules and by ind ΛΛ\Lambdaro nehemiah manufacturing coWebusers.uoi.gr - University of Ioannina nehemiah madison wisconsinWebFeb 2, 2010 · Abstract. Contravariantly finite resolving subcategories of the category of finitely generated modules have been playing an important role in the representation theory of algebras. In this paper ... nehemiah leadership skills