Abstract
The notion of observation plays a central role in current theories of concurrency. In this paper we investigate observation from the point of view of observation structures and observations systems; the former represent the observable entities, the later specify the allowed observations and their outcome. The resulting categories enjoy many interesting properties. Here we concentrate mainly on the study of fixed points of functors and on the existence of final coalgebras. The main result is that every nontrivial (non-identically empty) functor on the category of sets gives rise in a canonical way to a functor on the category of observation structures having a unique fixed point. This result is then extended to functors with an arbitrary number of arguments, possibly covariant in some arguments and contravariant in others. It is also shown that the resulting category of coalgebras has a final coalgebra. These results suggest that the category of observation structures is very adequate for the study of the semantics of concurrency.
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