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.

I happen to have typeset a number of notes in the last three years, for both graduate and undergraduate courses. As they may be useful to someone else, I decided to publish them here. They haven't been checked by anyone besides me, let alone by my teachers. I take full responsibility for the errors appearing in them, and in case you found any of them, please let me know.

I'm happy to share LaTeX code as well, upon request.

The following are notes I took in Padua during 2019. Where due, credit is given to my teachers in each set of notes.

• Analisi Funzionale

  Sbobine delle videolezioni.

  Le note sono su GitHub per chi volesse contribuire o anche solo segnalare correzioni e refusi.

• Hamiltonian Mechanics

  A course in symplectic and Poisson geometry, with some theory of integrability plus a digression on deformation quantization. Red parts are still unclear.

  These notes were started by me and then evolved into a broader collaboration. They are now on GitHub to better handle the process and making them future-proof.