Galois connection

== English == === Alternative forms === Galois connexion === Etymology === From Galois (attributive form of Galois theory) + connection; ultimately after French mathematician Évariste Galois. Coined by Norwegian mathematician Øystein Ore in 1944, Galois connexions, Transactions of the American Mathematical Society, 55, pages 493-513. === Noun === Galois connection (plural Galois connections) (category theory, order theory) A type of correspondence between partially ordered sets (posets), also applicable to preordered sets. 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 → B {\displaystyle G:A\rightarrow B} and F : B → A {\displaystyle F:B\rightarrow A} by G ( a ) = { y ∈ Y | ∀ x ∈ a x ρ y } {\displaystyle G(a)=\left\{y\!\in \!Y|\forall x\!\in \!a\ x\rho y\right\}} and F ( b ) = { x ∈ X | ∀ y ∈ b x ρ y } {\displaystyle F(b)=\left\{x\!\in \!X|\forall y\!\in \!b\ x\rho y\right\}} . Then ( F , G ) {\displaystyle (F,G)} is called a Galois connection of the first kind. ==== Hypernyms ==== adjunction ==== Hyponyms ==== isotone Galois connection, monotone Galois connection antitone Galois connection