A graveyard/dump for work in progress or just set of notes that deserve to be out there.
- Notes on categorical systems theory
Categorical systems theory (CST) (now DOTS) is a doubly-categorical framework for approaching and developing structural theories of systems and behaviour of any kind. These notes are meant to be (1) a basic reference for CST and (2) a source of examples and working developments. They're under active development, so quite far from camera-ready, and possibly never complete.
- Bayesian open games, diegetically
A draft on extending the ideas of Diegetic Representation of Feedback in Open Games to the Bayesian case, basically working out the definition of Nashator for this setting.
- Formal Observability and Behavioural Equivalence
A theory of observability in the formal framework of CST.
- A fibrational vocabulary for goal-directed systems
Marrying categorical logic and CST to talk about goals over systems, with some thoughts about how to express regulation goals.
- The universal property of external choice
External choice of parameterised maps feels like a coproduct but it's not. It turns out it's a 'soft coproduct', which is a 2-dimensional version of the coproduct whose universal property (which is a representability property) is weakened to an adjunction.
In the future, I plan to further explore this idea of embracing the second dimension of Para fully, for instance by working out how Kan extensions/lifts can be used to characterize goal-seeking behaviour.