Operational Galois adjunctions

Details Operational Galois adjunctions Operational Galois adjunctions

2000-08-03

arxiv.org/abs/quant-ph/0008021v1

Physics

Quantum Physics

24 pages - survey with proofs; Chapter of the volume: 'Current Research in Operational Quantum Logic: Algebras, Categories, La

Scientific paper

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.

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