Effect algebras, witness pairs and observables

4 pages•Published: July 28, 2014

Abstract

The category of effect algebras is the Eilenberg-Moore category for the
monad 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.

Links:	https://easychair.org/publications/paper/8hV
	https://doi.org/10.29007/71gb

BibTeX entry

@inproceedings{TACL2013:Effect_algebras_witness_pairs,
  author    = {Gejza Jenča},
  title     = {Effect algebras, witness pairs and observables},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/8hV},
  doi       = {10.29007/71gb},
  pages     = {109-112},
  year      = {2014}}

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