منابع مشابه
On Reflective Subcategories of Locally Presentable Categories
Are all subcategories of locally finitely presentable categories that are closed under limits and λ-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case λ = א0 the answer is affirmative also for all iso-full subcategories, i. e., those containing with every pair of objects all isomorphisms between them. We discuss...
متن کاملExtensions of covariantly finite subcategories
Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is covariantly finite. We give an example to show that Gentle–Todorov’s theorem may fail in an arbitrary abelian category; however we prove a triangulated version of Gentle–Todorov’s theorem which holds for arbitrary triangulated categories; we ...
متن کاملThe Homological Theory of Contravariantly Finite Subcategories:
Let C be an abelian or exact category with enough projectives and let P be the full subcategory of projective objects of C . We consider the stable category C/P modulo projectives, as a left triangulated category [14], [36]. Then there is a triangulated category S(C/P) associated to C/P, which is universal in the following sense. There exists an exact functor S : C/P -t S(C/P) such that any exa...
متن کاملContravariantly Finite Resolving Subcategories over Commutative Rings
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 we study contravariantly finite resolving subcategories over commutative rings. The main purpose of this paper is to classify contravariantly finite resolving subcategories over a henselian Gorenstein local ring;...
متن کاملOn Extensions of Covariantly Finite Subcategories
We prove that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is still covariantly finite. This extends a result by Sikko and Smalø. We also prove a triangulated version of the result. As applications, we obtain short proofs to a classical result by Ringel and a recent result by Krause and Solberg. 1. Main Theorems Let C b...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1985
ISSN: 0022-4049
DOI: 10.1016/0022-4049(85)90073-8