  A probabilistic structure on sequential dynamical systems is introduced here,
the new model will be called Probabilistic Sequential Network, PSN. The
morphisms of Probabilistic Sequential Networks are defined using two algebraic
conditions. It is proved here that two homomorphic Probabilistic Sequential
Networks have the same equilibrium or steady state probabilities if the
morphism is either an epimorphism or a monomorphism. Additionally, the proof of
the set of PSN with its morphisms form the category PSN, having the category of
sequential dynamical systems SDS, as a full subcategory is given. Several
examples of morphisms, subsystems and simulations are given.
