On evolution operators of genetic coalgebras.

We characterize evolutionary operators acting on coalgebras with genetic realization modeling the backwards genetic inheritance in Mendelian genetic systems. This characterization is made in terms of the different slices of the cubic stochastic matrix of type (1,2) given by the transition probabilities defining the genetic coalgebra comultiplication. We use the obtained characterization to describe all possible equilibrium states a genetic population can reach when tracing the genetic information one generation back.