Definition Dynamical system with interface A [efr-0028]

Let A be an arena. A dynamical system with interface A is an object S \in \mathcal {C} and a lens TS \leftrightarrows A. A morphism of systems is a map S \to S' so that this square commutes in \mathsf {\mathbb Arena}:

The category of systems with interface A is denoted \mathsf {Sys}(A)