Foulis Quantales and Complete Orthomodular Lattices

• Autoři: BOTUR Michal; PASEKA Jan; SMOLKA Richard
• Rok publikování: 2025
• Druh: Článek ve sborníku
• Konference: Advances in Fuzzy Logic and Technology : 14th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2025, Riga, Latvia, July 21–25, 2025, Proceedings, Part I
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://link.springer.com/chapter/10.1007/978-3-031-97225-6_25
• Doi: https://doi.org/10.1007/978-3-031-97225-6_25
• Klíčová slova: dagger category; Foulis semigroup; linear map; orthomodular lattice; quantale; quantale module; Sasaki projection
• Popis: Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales. Firstly, given a complete orthomodular lattice X, we associate with it a Foulis quantale Lin(X) consisting of its endomorphisms. This allows us to view X as a left module over Lin(X), thereby introducing a novel fuzzy-theoretic perspective to the study of complete orthomodular lattices. Conversely, for any Foulis quantale Q, we associate a complete orthomodular lattice [Q] that naturally forms a left Q-module. Furthermore, there exists a canonical homomorphism of Foulis quantales from Q to Lin([Q]).

Související projekty

• Specifický výzkum v odborné, aplikované a učitelské matematice 2024