Galois connection

plural Galois connections · alternative Galois connexion

1. category theoryA type of correspondence between partially ordered sets (posets), also applicable to preordered sets.

   Finally, we discuss Galois connections. It is interesting to note that these definitions can be found in Birkhoff (1940, 1948, 1967) under the heading of "polarities," and Everett (1944) showed that all Galois connections defined on power sets can be obtained from polarities.

   2001, J. Michael Dunn, Gary M. Hardegree, Algebraic Methods in Philosophical Logic, Oxford University Press, page 398

   2 more examples

   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 and F:B→A by G(a)=y!∈!Y|∀x!∈!axρy and F(b)=x!∈!X|∀y!∈!bxρy. Then (F,G) is called a Galois connection of the first kind.

   Galois connections appear in several areas of mathematics and computer science, and their applications. A Galois connection between sets X and Y is a pair #92;left#92;langle#92;uparrow,#92;downarrow#92;right#92;rangle of mappings #92;uparrow assigning subcollections of Y to subcollections of X, and #92;downarrow assigning subcollections of X to subcollections of Y.

   2006, Radim Bělohlávek, Taťána Funioková, Vilém Vychodil, “Galois connections with Truth Stressers: Foundations for Formal Concept Analysis of Object-Attribute Data with Fuzzy Attributes”, in Bernd Reusch, editor, Computational Intelligence, Theory and Applications: International Conference, Proceedings, Springer,, page 205