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Operational Galois Adjunctions

  • Bob Coecke
  • David Moore
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 111)

Abstract

We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its implementation at the level of quantaloids we consider some standard universal constructions and the extension of adjunctions to weak morphisms. Second, we present the categorical formulation of closure operators and introduce a hierarchy of contextual enrichments of the quantaloid of complete join lattices. Third, we briefly survey physical state-property duality and the categorical analysis of derived notions such as causal assignment and the propagation of properties.

Keywords

Closure Operator Natural Transformation Category Theory Complete Lattice Coherence Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Bob Coecke
    • 1
  • David Moore
    • 2
  1. 1.Department of MathematicsFree University of BrusselsBrusselsBelgium
  2. 2.Department of Theoretical PhysicsUniversity of GenevaGeneva 4Switzerland

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