Information Systems and the Theory of Categories : Is Every Model an Anticipatory System?

The possible unknown behaviour of a reactive system may not be fully understood but it may be modelled in an information system. The relationship between a system and its model can be constructed through a series of stages showing the correlation between arrows in the system and in the model. Such a diagram is formal where the system and the model are 2-cell categories and the mappings between the system and the model are adjunctions. Such mappings can be built up using basic arrow constructions or given in a more abstract form in terms of freeness and co-freeness. The adequacy of a model as a representation of a natural system is discussed in terms of mapping properties such as reflection, isomorphism and adjoint equivalence. The circumstances for the model being anticipatory are considered.