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Galois connection

Galois connection noun: a type of correspondence between partially ordered sets (posets), also applicable to preordered sets.

Noun

Galois connection (plural Galois connections)

  1. A type of correspondence between partially ordered sets (posets), also applicable to preordered sets.
    • 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.1986, Horst Herrlich, Miroslav Hušek, Galois Connections, Austin Melton, Mathematical Foundation of Programming Semantics: International Conference, Proceedings, Springer, Lecture Notes in Computer...
    • 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

Forms of Galois connection

pluralGalois connections
alternative formGalois connexion

Origin of Galois connection

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.

Questions about Galois connection

What does Galois connection mean?
Galois connection means a type of correspondence between partially ordered sets (posets), also applicable to preordered sets.
What part of speech is Galois connection?
Galois connection is a noun.
What is the plural of Galois connection?
The plural of Galois connection is Galois connections.

Words near Galois connection in the dictionary

  1. galoche
  2. galoched
  3. galoches
  4. galocitabine
  5. Galois
  6. Galois connection
  7. Galois connections
  8. Galois extension
  9. Galois extensions
  10. Galois field
  11. Galois fields

Source and license

Adapted from Wiktionary: Galois connection (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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