ABSTRACT
Clones can then be characterized as Galois-closed sets of operations, that is, sets F having the property that PolInvF = F (see R. Poschel and L. A. Kalu'inin, [96]). Dually, closed sets R of relations satisfying InvPolR = R are called relational clones. There is also an algebraic characterization of relational clones using certain operations defined on sets of relations ([96]). As we saw in Section 6.1, the two classes of closed sets of a Galois-connection form complete lattices which are dually isomorphic to each other. In the specific case of clones of operations, we see that the set of all clones of operations defined on a base set A forms a complete lattice LA; moreover this lattice is dually isomorphic to the lattice of all relational clones on A.
