Publication details
Foulis Quantales and Complete Orthomodular Lattices
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Proceedings |
| Conference | 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 |
| MU Faculty or unit | |
| Citation | |
| web | 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 |
| Keywords | dagger category; Foulis semigroup; linear map; orthomodular lattice; quantale; quantale module; Sasaki projection |
| Description | 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]). |
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