Towards Foundations of Categorical Cybernetics — Matteo Capucci, Bruno Gavranović, Jules Hedges & Eigil Fjeldgren Rischel (2021). arXiv:2105.06332 (v2, PDF); EPTCS 372, 2022, pp. 235-248.
Proposes a common categorical foundation for systems that act and learn: parametrised morphisms ( over an actegory) combined with optics, so that gradient-based learners, Bayesian agents and open games are all parametrised optics differing in the backward structure; open games add a selection functor for best responses.
Sources: the paper, arXiv:2105.06332v2, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Definition 1: actegory; Definition 2: ; Remarks 3–4: reparametrisation, CoPara
- Proposition 5: Para is a monad on actegories
- Definition 8: optics
- §4: open games as parametrised optics with selection functions
Concept notes
Actegory, Para Construction, Optic, Open Game, Double Category