I have recently read Abramsky and Heunen's paper on Operational structures and categorical physics. I have been looking at operational structures as internal categories in a monoidal category like we find here. We see that internal categories can be seen as monads in the category of comonoids in a monoidal category. These internal categories represent the foundation of a simplified quantum field theory if we think of Vicary's paper on the Quantum Harmonic Oscillator. In particular, I think of the internal categories as structural probes of arbitrary complexity and the functor from the underlying monoidal category to the little internal cats as probes of "quantum causal structure" which we "see" in terms of diagrams in the internal category. The internal category is seen as an apparatus, and we probe underlying structure by mapping diagrams into our little (internal) test categories. That is how I see operationalism right now. My question is about Chu spaces, as Abramsky uses them. Can we find the authors' special subcategory of the category of Chu spaces, as an internal category in a monoidal category? I would like to think that my ideas are not that far off from what Abramsky has done and this would be a start.
