Galois connection
For an order theoretic example, let be some set, and let and both be the power set of , ordered by inclusion. Pick a fixed subset of . Then the maps and , where , and , form a monotone Galois connection, with being the lower adjoint. A similar Galois connection whose lower adjoint is given by the meet (infimum) operation can be found in any Heyting algebra. Especially, it is present in any Boolean algebra, where the two mappings can be described by and . In logical terms: "implication from " is the upper adjoint of "conjunction with ".