Titlebook: Current Research in Operational Quantum Logic; Algebras, Categories Bob Coecke,David Moore,Alexander Wilce Book 2000 Springer Science+Busin

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Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics . = . × ... In this expository article (supplementary to the individual contributions of the authors), we outline the theory of such free extensions, and the parallel notion of the unitary representation of . induced by a unitary representation of .. To keep matters simple, we restrict our attentio

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Short Introduction to Enriched Categoriesa compact fashion, we have brought together in the first part of this paper the definitions and basic properties of such notions as limit and colimit constructions in a category, adjoint functors between categories, equivalences and monads. In the second part we pass on to enriched category theory:

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Operational Galois Adjunctionss 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 operato

Forsake

Operational Axiomatics and Compound Systemssical results of Aerts and Daubechies on the propositional representation of compound physical systems are analyzed from a categorical point of view. The problems of the basic postulates in the case of the separated product lead to the construction of a category consisting of objects with somewhat l

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Quantales and Observational Semanticsrch in computer science where this idea has been used. We extend the mathematical framework hitherto available so that it can be applied to more general systems than before, in particular to quantum systems and systems whose behaviour is partially unobservable.

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Quantum Languagesa. Of particular interest are the deterministic automata and the regular languages that they accept. We also consider reversible deterministic automata which accept a smaller class of languages called the reversible languages and probabilistic automata which accept a larger class. We show that rever

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Operational Galois Adjunctionsrs 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.

Microaneurysm

Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics and the parallel notion of the unitary representation of . induced by a unitary representation of .. To keep matters simple, we restrict our attention almost wholly to actions of finite groups on finite sets and finite-dimensional unitary spaces.