10 papers
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…
Quantales carrying ortholattice structure
Michal Botur, David Kruml, Jan Paseka
This paper investigates the intersection of residuated structures from many-valued logic and orthomodular lattices from quantum logic. We explore whether non-Boolean structures can…
Axiomatising the dagger category of complex Hilbert spaces
Jan Paseka, Thomas Vetterlein
We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy…
Dagger categories of orthosets and the complex Hilbert spaces
Jan Paseka, Thomas Vetterlein
An orthoset is a non-empty set together with a symmetric binary relation and a constant such that for any , and for any . M…
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…
Characterisation of quadratic spaces over the Hilbert field by means of the orthogonality relation
Miroslav Korbelář, Jan Paseka, Thomas Vetterlein
An orthoset is a set equipped with a symmetric, irreflexive binary relation. With any (anisotropic) Hermitian space , we may associate the orthoset , consisting of…
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…
Adjointable maps between linear orthosets
Jan Paseka, Thomas Vetterlein
Given an (anisotropic) Hermitian space , the collection of at most one-dimensional subspaces of , equipped with the orthogonal relation and the zero linear sub…
Categories of orthosets and adjointable maps
Jan Paseka, Thomas Vetterlein
An orthoset is a non-empty set together with a symmetric and irreflexive binary relation , called the orthogonality relation. An orthoset with 0 is an orthoset augmented wit…