6 papers
Categorical Equivalence Between Finitary Orthomodular Dynamic Algebras and Orthomodular Lattices
Juanda Kelana Putra, Richard Smolka
This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the…
On -based orthomodular dynamic algebras
Jan Paseka, Juanda Kelana Putra, Richard Smolka
This paper establishes a categorical equivalence between the category of complete orthomodular lattices and the category of -b…
Many-valued aspects of tense an related operators
Michal Botur, Jan Paseka, Richard Smolka
Our research builds upon Halmos's foundational work on functional monadic Boolean algebras and our previous work on tense operators to develop three essential constructions, includ…
Foulis quantales and complete orthomodular lattices
Michal Botur, Jan Paseka, Richard Smolka
Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales. Firstly, given a complete orthomodular lattice X, we associ…
A dagger kernel category of complete orthomodular lattices
Michal Botur, Jan Paseka, Richard Smolka
Dagger kernel categories, a powerful framework for studying quantum phenomena within category theory, provide a rich mathematical structure that naturally encodes key aspects of qu…
Another look on tense and related operators
Michal Botur, Jan Paseka, Richard Smolka
Motivated by the classical work of Halmos on functional monadic Boolean algebras we derive three basic sup-semilattice constructions, among other things the so-called powersets and…