published with Bas Westerbaan and John van de Wetering [ arxiv ]

Some are neither Boolean, nor quite convex.

published with Bas Westerbaan and John van de Wetering [ arxiv ]

A representation theory for ω-directed complete effect monoids.

published with Luuk Hendriks [ arxiv · repos · website ]

Includes the “lizard” trick.

printed supervised by Bart Jacobs [ github · arxiv · ru ]

Includes an introduction to the theory of C*-algebras and von Neumann algebras.

published with Bas Westerbaan and John van de Wetering [ arxiv ]

The title says it all.

published with Bas Westerbaan, Rutger Kuyper, Carst Tankink, Remy Viehoff, and Henk Barendregt [ arxiv · preprint ]

A simplification and slight extension of Statman’s Hierarchy Theorem.

published with Bart Jacobs [ arxiv ]

Featuring the metric completeness of of ω-complete effect modules.

published with Bas Westerbaan [ arxiv · preprint ]

We give a universal property for Paschke’s (and Stinespring’s) dilation.

published with Bas Westerbaan [ arxiv · preprint ]

We axiomatise the sequential product on von Neumann algebras.

unpublished with Kenta Cho [ arxiv · preprint · extended abstract ]

We interpret Selinger and Valiron’s quantum lambda calculus in the category of completely positive normal subunital maps between von Neumann algebras, and prove that the interpretation is adequate with respect to operational semantics.

unpublished with Kenta Cho [ arxiv · preprint ]

We describe the free commutative monoid on the category of von Neumann algebras

done with Kenta Cho, Bart Jacobs, and Bas Westerbaan [ arXiv ]

What would happen if one replaced subobjects S↣X by predicates X→1+1?

published with Kenta Cho, Bart Jacobs, and Bas Westerbaan [ arxiv · preprint · video · slides ]

A universal property for A ↦ √B A √B appears in a chain of adjunctions.

published with Bart Jacobs [ preprint · slides ]

The step from probability measure to integral gets a universal property with the aid of ω-complete effect algebras and ω-complete effect modules.

unpublished with Kenta Cho, Bart Jacobs, and Bas Westerbaan [ preprint ]

A universal property for A ↦ √B A √B appears in a chain of adjunctions.

published [ arxiv · preprint ]

The category of positive unital linear maps between C*-algebras is the Kleisli category of a comonad on the subcategory of unital *-homomorphisms between C*-algebras.

published with Bart Jacobs and Bas Westerbaan [ preprint · slides ]

Convex sets appear as state spaces of computation in an effectus, and form an effectus.

published with Henning Kerstan and Barbara König [ preprint ]

Our take on when an adjunction can be lifted to coalgebras, with many examples.

published with Alexandra Silva [ preprint · slides ]

Study of a generalisation of the removal of ε-transitions from a non-deterministic automaton.

done supervised by prof. A.C.M. van Rooij [ arxiv ]

Simultaneous study of measure and integral using lattices and uniform spaces.