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Foulis m-Semilattices and Quantale Modules from Orthomodular Lattices

Shows the category of orthomodular lattices with linear maps is a dagger category and, for each orthomodular lattice X, builds a Foulis m-semilattice Lin(X) of endomorphisms that forms a quantale, so X becomes a left Lin(X)-module, bringing the fuzzy-set/quantale-module framework to orthomodular-lattice (quantum-logic) theory.

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Foulis m-semilattices and their modules Michal Botur

Building on work of Jacobs, this paper shows that the category OMLatLin of orthomodular lattices with linear maps is a dagger category (it carries an involution reversing arrows). For each orthomodul…