8 papers
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…