5 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…
Characterisation of quadratic spaces over the Hilbert field by means of the orthogonality relation
Miroslav KorbeláÅ, 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…
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…
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…