Publications (43)
Universal Properties in Quantum Theory
Mathieu Huot, Sam Staton
We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basi…
Concrete categories and higher-order recursion (With applications including probability, differentiability, and full abstraction)
Cristina Matache, Sean Moss, Sam Staton
We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such a…
Relating coalgebraic notions of bisimulation
Sam Staton
The theory of coalgebras, for an endofunctor on a category, has been proposed as a general theory of transition systems. We investigate and relate four generalizations of bisimulat…
Monads for Measurable Queries in Probabilistic Databases
Swaraj Dash, Sam Staton
We consider a bag (multiset) monad on the category of standard Borel spaces, and show that it gives a free measurable commutative monoid. Firstly, we show that a recent measurabili…
A causal Markov category with Kolmogorov products
Sean Moss, Sam Staton
In Fritz & Rischel, Infinite products and zero-one laws in categorical probability, the problem was posed of finding an interesting Markov category which is causal and has all (sma…
The Relative Monadic Metalanguage
Jack Liell-Cock, Zev Shirazi, Sam Staton
Relative monads provide a controlled view of computation. We generalise the monadic metalanguage to a relative setting and give a complete semantics with strong relative monads. Ad…