Abstract
Multicoreflective subcategories of a given category can be viewed as “categories of connected objects” for suitable connectivity notions. If one tries to define “connected objects” in an absolute way, one is led to the notion of coprime object. Both notions are treated using the same tool, which is parallel to the description of coreflective subcategories by projectivity. These methods can be applied to characterize multicoreflective subcategories of Comp. They also lead to some special results about reflective and multireflective subcategories of the category of unital rings. In particular, the category of powers of 7L is reflective if and only if there exists no uncountable measurable cardinal.
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