11 papers
Vertex-transitive quantum graphs
Mac Hayes, Trevor Jess, Andre Kornell +1
We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classi…
Quantum graphs of homomorphisms
Andre Kornell, Bert Lindenhovius
We introduce a category of quantum graphs, whose definition is motivated entirely from noncommutative geometry. For all quantum graphs and in $\mathsf{qGph}…
A category of quantum posets
Andre Kornell, Bert Lindenhovius, Michael Mislove
We investigate a category of quantum posets that generalizes the category of posets and monotone functions. Up to equivalence, its objects are hereditarily atomic von Neumann algeb…
Categories of quantum cpos
Andre Kornell, Bert Lindenhovius, Michael Mislove
This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of…
A new characterization of Kac-type discrete quantum groups
Alexandru Chirvasitu, Andre Kornell
We obtain two related characterizations of discrete quantum groups and discrete quantum groups of Kac type as allegorical group objects in the symmetric monoidal dagger category of…
The quantum Ramsey numbers
Andrew Allen, Andre Kornell
Operator systems of matrices can be viewed as quantum analogues of finite graphs. This analogy suggests many natural combinatorial questions in linear algebra. We determine the qua…