Towards foundations of categorical cybernetics

Matteo Capucci, Bruno Gavranovic, Julian Hedges, Eigil Fjeldgren Rischel

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We propose a categorical framework for processes which interact bidirectionally with both an environment and a ‘controller’. Examples include open learners, in which the controller is an optimiser such as gradient descent, and an approach to compositional game theory closely related to open games, in which the controller is a composite of game-theoretic agents. We believe that ‘cybernetic’ is an appropriate name for the processes that can be described in this framework.
Original languageEnglish
Number of pages13
Publication statusPublished - 12 Jul 2021
EventApplied Category Theory 2021 - University of Cambridge, Cambridge, United Kingdom
Duration: 12 Jul 202116 Jul 2021


ConferenceApplied Category Theory 2021
Country/TerritoryUnited Kingdom


  • cybernetics
  • categorical framework
  • bidirectional interaction

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