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Hereditarity of closure operators and injectivity

Gabriele Castellini, Eraldo Giuli (1992)

Commentationes Mathematicae Universitatis Carolinae

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 𝒜 . It is shown that, if every object of 𝒜 is a subobject of an 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.

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