Editing Galois connection (section)

====Lattices====
Further interesting examples for Galois connections are described in the article on [[completeness (order theory)|completeness properties]]. Roughly speaking, the usual functions ∨ and ∧ are lower and upper adjoints to the [[diagonal map]] {{math|''X'' → ''X'' × ''X''}}. The least and greatest elements of a partial order are given by lower and upper adjoints to the unique function {{math|''X'' → {1}.}} Going further, even [[complete lattice]]s can be characterized by the existence of suitable adjoints. These considerations give some impression of the ubiquity of Galois connections in order theory.