In the following, we consider a (monotone) Galois connection , where is the lower adjoint as introduced above. Some helpful and instructive basic properties can be obtained immediately. By the defining property of Galois connections, is equivalent to , for all in . By a similar reasoning (or just by applying the duality principle for order theory), one finds that , for all in . These properties can be described by saying the composite is "deflationary", while is "inflationary" (or "extensive").