Phrase guide

Galois connection

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Topics: category-theory, computing, engineering, mathematics, natural-sciences, order-theory, physical-sciences, sciences

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.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

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.