  We describe here the new concept of $\epsilon$-Homomorphisms of Probabilistic
Regulatory Gene Networks(PRN). The $\epsilon$-homomorphisms are special
mappings between two probabilistic networks, that consider the algebraic action
of the iteration of functions and the probabilistic dynamic of the two
networks. It is proved here that the class of PRN, together with the
homomorphisms, form a category with products and coproducts. Projections are
special homomorphisms, induced by invariant subnetworks. Here, it is proved
that an $\epsilon$-homomorphism for 0 <$\epsilon$< 1 produces simultaneous
Markov Chains in both networks, that permit to introduce the concepts of
$\epsilon$-isomorphism of Markov Chains, and similar networks.
