Precategories for combining probabilistic automata

Abstract A relaxed notion of category is presented having in mind the categorical caracterization of the mechanisms for combining probabilistic automata, since the composition of the appropriate morphisms is not always defined, A detailed discussion of the required notion of morphism is provided. The partiality of composition of such morphisms is illustrated at the abstract level of countable probability spaces. The relevant fragment of the theory of the proposed precategories is developed, including (constrained) products and Cartesian liftings. Precategories are precisely placed in the universe of neocategories. Some classical results from category theory are shown to carry over to precategories. Other results are shown not to hold in general. As an application, the precategorical universal constructs are used for characterizing the basic mechanisms for combining probabilistic automata: aggregation, interconnection and state constraining.