Minimal residuated mappings on lattices

If L is a complete lattice then a mapping f: L\to L is called residuated if it preserves all joins. Obviously the set Res(L) of all residuated mappings on L is a lattice with respect to the pointwise defined order relation. Our aim is to collect information about atoms of the lattice Res(L). We start with motivation by telling how these atoms are connected with the problem of describing order affine complete lattices.