Galois connection

Etymology
From (attributive form of ) + ; ultimately after French mathematician. Coined by Norwegian mathematician in 1944, Galois connexions, , 55, pages 493-513.

Noun

 * 1)  A type of correspondence between partially ordered sets (posets), also applicable to preordered sets.
 * 2) * 1986, Horst Herrlich, Miroslav Hušek, Galois Connections, Austin Melton, Mathematical Foundation of Programming Semantics: International Conference, Proceedings, Springer, Lecture Notes in Computer Science: 239, page 122,
 * Define maps $$G: A\rightarrow B$$ and $$F: B\rightarrow A$$ by $$G(a)=\left\{ y\!\in\!Y |\forall x\!\in\! a\ x\rho y\right\}$$ and $$F(b)=\left\{ x\!\in\!X |\forall y\!\in\! b\ x\rho y\right\}$$. Then $$(F,G)$$ is called a Galois connection of the first kind.