Foundations of Physics

, Volume 34, Issue 7, pp 1063–1090

Quantum Event Structures from the Perspective of Grothendieck Topoi

Authors

  • Elias Zafiris
    • Faculty of Mathematics and InformaticsUniversity of Sofia
    • Institute of Mathematics PanepistimiopolisUniversity of Athens
Article

DOI: 10.1023/B:FOOP.0000037623.08379.df

Cite this article as:
Zafiris, E. Foundations of Physics (2004) 34: 1063. doi:10.1023/B:FOOP.0000037623.08379.df
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Abstract

We develop a categorical scheme of interpretation of quantum event structures from the viewpoint of Grothendieck topoi. The construction is based on the existence of an adjunctive correspondence between Boolean presheaves of event algebras and Quantum event algebras, which we construct explicitly. We show that the established adjunction can be transformed to a categorical equivalence if the base category of Boolean event algebras, defining variation, is endowed with a suitable Grothendieck topology of covering systems. The scheme leads to a sheaf theoretical representation of Quantum structure in terms of variation taking place over epimorphic families of Boolean reference frames.

quantum event structuresBoolean reference framestoposadjunctionsheavesGrothendieck topology
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© Plenum Publishing Corporation 2004