Galois connection

English Alternative forms en Galois connexion Etymology From en Galois (attributive form of en Galois theory) + en 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 en 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 and by and . Then is called a Galois connection of the first kind. en 2001 J. Michael Dunn; Gary M. Hardegree Algebraic Methods in Philosophical Logic https://books.google.com.au/books?id=-AokWhbILUIC&pg=PA398&dq=%22Galois+connection%22%7C%22Galois+connections%22&hl=en&sa=X&ved=0ahUKEwjJqKbw5p_aAhVJhpAKHRUTDiMQ6AEIbzAO#v=onepage&q=%22Galois%20connection%22%7C%22Galois%20connections%22&f=false 398 w:Oxford University Press 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. en 2006 Radim Bělohlávek; Taťána Funioková; Vilém Vychodil Galois connections with Truth Stressers: Foundations for Formal Concept Analysis of Object-Attribute Data with Fuzzy Attributes Bernd Reusch Computational Intelligence, Theory and Applications: International Conference, Proceedings Springer, https://books.google.com.au/books?id=NyIguQjGk-MC&pg=PA205&dq=%22Galois+connection%22%7C%22Galois+connections%22&hl=en&sa=X&ved=0ahUKEwjJqKbw5p_aAhVJhpAKHRUTDiMQ6AEIPjAE#v=onepage&q=%22Galois%20connection%22%7C%22Galois%20connections%22&f=false 205 Galois connections appear in several areas of mathematics and computer science, and their applications. A Galois connection between sets and is a pair of mappings assigning subcollections of to subcollections of , and assigning subcollections of to subcollections of . Hypernyms en adjunction Hyponyms en isotone Galois connection, en monotone Galois connection en antitone Galois connection en eponyms