  We consider the notions of the replicators, including the duplicator and
triplicator, of a binary operad. As in the closely related notions of
di-Var-algebra and tri-Var-algebra in [14], they provide a general operadic
definition for the recent constructions of replicating the operations of
algebraic structures. We show that taking replicators is in Koszul dual to
taking successors in [3] for binary quadratic operads and is equivalent to
taking the white product with certain operads such as Perm. We also relate the
replicators to the actions of average operators.
