WORKSHOP

Applied category theory is always the same. Take a field, reformulate everything into the language of categories and then you get an abstract analog of your theory that you can reuse in another setting, where you are guaranteed that all statements still make sense, but with a new meaning.

Recently, we started to apply this methodology to symbolic dynamics with the goal to derive an abstract theory that would encompass the classical, probabilistic and quantum setting in one go.

The goal of this workshop is to extend our formalism, based on diagrammatic equations.
After defining a universal and complete language for one-dimensional sofic subshifts, our goal is to be able to write equations about other kinds of subshifts: subshifts of finite type, effective, substitutive, … Another goal is to start developing the formalism in a new setting: probabilistic (diagram describing sets of measures on subshifts for example) and even quantum. Last, we want to formulate many classical proofs of symbolic dynamics on our formalism, with the hope that their diagrammatic formulation may naturally be applied in many other settings (probabilistic, quantum, …).