Geodesic
Hereditarity of closure operators and injectivity
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 149-157 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let $C$ be a regular closure operator induced by a subcategory $\Cal A$. It is shown that, if every object of $\Cal A$ is a subobject of an $\Cal A$-object which is injective with respect to a given class of monomorphisms, then the closure operator $C$ is hereditary with respect to that class of monomorphisms.
A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let $C$ be a regular closure operator induced by a subcategory $\Cal A$. It is shown that, if every object of $\Cal A$ is a subobject of an $\Cal A$-object which is injective with respect to a given class of monomorphisms, then the closure operator $C$ is hereditary with respect to that class of monomorphisms.
Classification : 18A20, 18A32, 18G05
Keywords: closure operator; hereditary closure operator; injective object; factorization pair 
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Castellini, Gabriele; Giuli, Eraldo. Hereditarity of closure operators and injectivity. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 149-157. http://geodesic.mathdoc.fr/item/CMUC_1992_33_1_a16/

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