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Given suitable categories T, C and functor F : T → C, if X,Y are objects of T, then we define an (X,Y)-relation in C to be a triple $$\left( {R,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} ,\bar r} \right)$$ , where R is an object of C and r : R → FX and are morphisms of C. We define an algebra of relations in C, including operations of “relabeling,” “sequential composition,” “parallel composition,” and “feedback,” which correspond intuitively to ways in which processes can be composed into networks. Each of these operations is defined in terms of composition and limits in C, and we observe that any operations defined in this way are preserved under the mapping from relations in C to relations in C′ induced by a continuous functor G : C → C′.

To apply the theory, we defined a category Auto of concurrent automata, and we give an operational semantics of dataflow-like networks of …