Foundations of Physics

, Volume 34, Issue 7, pp 1063–1090 | Cite as

Quantum Event Structures from the Perspective of Grothendieck Topoi

  • Elias Zafiris
Article

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 structures Boolean reference frames topos adjunction sheaves Grothendieck topology 

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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • Elias Zafiris
    • 1
    • 2
  1. 1.Faculty of Mathematics and InformaticsUniversity of SofiaSofiaBulgaria
  2. 2.Institute of Mathematics PanepistimiopolisUniversity of AthensAthensGreece

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