Abstract

We study some particular examples of quantaloids and corresponding morphisms, originating from primitive physical reasonings on the lattices of properties of physical systems. AMS classification code: 03G10, 18D20, 81P10. Key words: Complete Lattice, Galois Adjoint, Physical System, Quantaloid. 1 Introduction The starting point for our research program is the fact, already observed in Eilenberg and Mac Lane's seminal paper [8], that preordered sets may be considered as small thin categories. One can then not only reformulate a large part of the theory of order structures in categorical terms, but also apply general categorical techniques to specific order theoretic problems. In particular, the notion of an adjunction reduces to that of a residuation [15] 4.5, whereas the notion of a monad reduces to that of a closure operator [15] 6.1-2. Now the above categorical notions have direct physical interpretations in the context of axiomatic quantum theory, the order relation in the prop...

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