Lattices
Further interesting examples for Galois connections are described in the article on completeness properties. It turns out that the usual functions and are adjoints in two suitable Galois connections. The same is true for the mappings from the one element set that point out the least and greatest elements of a partial order. 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.
Read more about this topic: Galois Connection, Examples, Order Theory