A simple system is in general a bounded, but not necessarily closed, entity- here represented as a category of stable, interacting components with inputs and outputs from the system's environment, or as a supercategory for a complex system consisting of subsystems, or components, with internal boundaries among such subsystems. In order to define a `system' one therefore needs to specify the following data:

1. components or subsystems;
2. mutual interactions, relations or links;
3. a separation of the selected system by some boundary which distinguishes the system from its environment, without necessarily `closing' the system to material exchange with its environment;
4. the specification of the system's environment;
5. the specification of the system's categorical structure and dynamics (a supercategory will be required only when either the components or subsystems need be themselves considered as represented by a category , i.e. the system is in fact a super-system of (sub)systems, as it is the case of emergent super-complex systems or organisms).

A general dynamic system $S_{GD}$ is a quintuple $([I,O], [\lambda: I \to O], \R_S , [\Delta: \R_S \to \R_S], \grp_B)$ , where:

1. $I$ and $O$ are, respectively, the input and output manifolds of the system , $S_{GD}$ ;
2. $\R_S$ is a category with structure determined by the components of $S_{GD}$ as objects and with the links or relations between such components as morphisms;
3. $\Delta: \R_S \to \R_S$ is the `dynamic transition' functor in the functor category $Aut_S$ of system endomorphisms (which is endowed with a groupoid structure only in the case of reversible, closed systems);
4. $\lambda$ is the output `function or map' represented as a manifold homeomorphism;
5. $\grp_B$ is a topological groupoid specifying the boundary, or boundaries, of $S_{GD}$ .