Closure operators, monomorphisms and epimorphisms in categories of groups
Compact objects surjectivity of epimorphisms and compactifications
Hereditarity of closure operators and injectivity
A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let be a regular closure operator induced by a subcategory . It is shown that, if every object of is a subobject of an -object which is injective with respect to a given class of monomorphisms, then the closure operator is hereditary with respect to that class of monomorphisms.
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