Download PDFOpen PDF in browserEffect algebras, witness pairs and observables4 pages•Published: July 28, 2014AbstractThe category of effect algebras is the Eilenberg-Moore category for themonad arising from the free-forgetful adjunction between categories of bounded posets and orthomodular posets. In the category of effect algebras, an observable is a morphism whose domain is a Boolean algebra. The characterization of subsets of ranges of observables is an open problem. For an interval effect algebra E, a witness pair for a subset of S is an object living within E that "witnesses existence" of an observable whose range includes S. We prove that there is an adjunction between the poset of all witness pairs of E and the category of all partially inverted E-valued observables. Keyphrases: effect algebra, observable, witness map In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 109-112.
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