Double Operadic Theory of Systems (DOTS), neé (Doubly) Categorical Systems Theory ((D)CST), is a formal mathematical theory of systems. A theory of systems is the algebra of a double operad: the operations of the operad describe how to compose systems, while the algebra substantiates these operations into actual functors between categories of systems. This structure combines both the compositional and structural aspects of systems theory, with the operad part describing compositionality and the categorical part describing the structure of systems.
DOTS being formal means we can work at a level of generality at which we can meanigfully talk about the subjects of systems theory—systems, processes, interfaces, behaviours, etc.—without ever having to commit to a specific way to model them (coalgebras, machines, decorated cospans, behaviour types, etc.).
I'm working on DOTS within the ARIA project 'Safeguarded AI' in close collaboration with Topos Research UK and the folks there (David Jaz Myers, Sophie Libkind, Jason Brown, José Siqueira, etc.)
Reading list
- Dynamical systems and sheaves, by David Spivak, Patrick Schultz, and Christina Vasilakopoulou
- Open Systems: A Double Categorical Perspective, by Kenny Courser
- Categorical Systems Theory, by David Jaz Myers
- Notes on Categorical Systems Theory, by me
- Towards a double operadic theory of systems, by David Jaz Myers and Sophie Libkind
- Representable Behaviour in Double Categorical Systems Theory, by me
- The most up to date account of DOTS is this lecture series by David Jaz Myers