Abstract
An extension operator “c” in a category is an assignment, to each object A a monomorphism c A : A→cA. Seeking to approximate such a c by a functor, in our earlier paper “Maximum monoreflections,” we showed that with some hypotheses on the category, and on c, there is a monoreflection μ(c) maximum beneath c. Thus, in a suitable category of rings, using the complete ring of quotients operator Q, each object A has a “maximum functorial ring of quotients” μ(Q)A. But the proof gave no hint of how to calculate the general μ(c)A's, nor the particular μ(Q)A's. In the present paper, we give an explicit formula (and separate proof of existence) for the μ(c)A's, under more complicated hypotheses on the category and assuming the c A 's are essential monomorphisms. We discuss briefly how the formula proves adequate to calculate the μ(Q)A's in Archimedean f-rings, and some related and necessary constructs in Archimedean l-groups.
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