Further interesting examples for Galois connections are described in the article on completeness properties. Roughly speaking, it turns out that the usual functions ∨ and ∧ are lower and upper adjoints to the diagonal map . The least and greatest elements of a partial order are given by lower and upper adjoints to the unique function Going further, even complete lattices can be characterized by the existence of suitable adjoints. These considerations give some impression of the ubiquity of Galois connections in order theory.