Abstract
The category of effect algebras is the Eilenberg-Moore category for themonad arising from the free-forgetful adjunction between categories of bounded posetsand orthomodular posets.In the category of effect algebras, an observable is a morphism whose domainis a Boolean algebra. The characterization of subsets of ranges of observables isan open problem.For an interval effect algebra E, a witness pair for a subset of S is an objectliving within E that "witnesses existence" of an observable whose rangeincludes S. We prove that there is an adjunction between the poset of allwitness pairs of E and the category of all partially inverted E-valuedobservables.
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