Geodesic
Galois Connections and Pair Algebras
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 498-501

Voir la notice de l'article provenant de la source Cambridge University Press

Unless further restricted, P, Q, and R denote arbitrary partially ordered sets whose order relations are all written “≦” .An isotone mapping φ: P → Q is said to be residuated if there is an isotone mapping ψ: Q → P such that(RM 1) xφψ ≧ x for all x i n P;(RM 2) yψφ ≦ for all y in Q.Let Q * denote the partially ordered set with order relation dual to that of Q.(A) The following conditions are equivalent:(i) φ: P → Q * is a Galois connection;(ii) φ: P → Q is a residuated mapping;(iii) Max{z ∈ P: zy ≦ y} exists for all y in Q and is equal to yψ.Since ψ is uniquely determined by φ, it will be denoted by φ +. 
Derderian, J. C. Galois Connections and Pair Algebras. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 498-501. doi: 10.4153/CJM-1969-056-x
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