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2022
Let C be a class of modules and L = lim C the class of all direct limits of modules from C. The class L is well understood when C consists of finitely presented modules: L then enjoys various closure properties. We study the closure properties of L in the general case when C is arbitrary class of modules. Then we concentrate on two important particular
Positselski, L. (Leonid) +2 more
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Let C be a class of modules and L = lim C the class of all direct limits of modules from C. The class L is well understood when C consists of finitely presented modules: L then enjoys various closure properties. We study the closure properties of L in the general case when C is arbitrary class of modules. Then we concentrate on two important particular
Positselski, L. (Leonid) +2 more
openaire +1 more source
Basic Properties of Closure Operators
1995Categorical closure operators as defined in this chapter for any category with a suitable subobject structure provide simultaneously a coherent closure operation for the subobjects of each object of the category. The notions of closedness and denseness associated with a closure operator are discussed from a factorization point of view.
D. Dikranjan, W. Tholen
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Closure operators with prescribed properties
1988The notion of closure operator on a category is explored, utilizing the approach of Dikranjan and Giuli. Conditions on the underlying factorization structure are given, which allow the construction of closure operators satisfying a variety of extra conditions.
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