We present the rudiments of a unifying theory of general processes encompassing discrete, continuous, and hybrid systems. The main focus is on the study of process behaviour, but constructions on processes are also considered in some detail. In particular, we show that processes admit an abstract, conceptual treatment of bisimilarity via the notion of open map (as advocated by Winskel et al.). Furthermore, we present a tool-kit of categorical constructions on processes that can be regarded as the basis of a process description language. Within the general theory, typical operations of process calculi on discrete and hybrid systems are discussed.
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