5 Category Based Approaches

The theory of categories provides a general theory of mathematical structures. CSNs, their components, behaviour, and properties can be seen as examples for abstractions of selected mathematical structures. In contrast to traditional algebraic approaches, relations between system objects are defined by comparison operators inside or between classes of similar system elements (categories). Morphisms, homologies, and functors act as comparison operators. Processes are encoded by sequences of natural transformations. Facets of similarities between biomolecules, their properties, and processing mechanisms can be modeled by category theory. This leads to systems of description logics, formal semantics as well as domain theory and methods for model checking, formal specification and verification on various levels of abstraction ([9]).