Galois connections and residuation: origins and
                 developments I

                                  Bernard Monjardet

    Centre d’Economie de la Sorbonne (University of Paris 1) and CAMS (Centre
                    Analyse et Mathmatique Sociale), France

Abstract. The equivalent notions of Galois connexions, and of residual and residuated
maps occur in a great varieties of “pure” as well as “applied” mathematical theories.
They explicitly appeared in the framework of lattice theory and the first of these talks
is devoted to the history of their appearance and of the revealing of their links in
this framework. So this talk covers more or less the period between 1940 (with the
notion of polarity defined in the first edition of Birkoff’s book Lattice theory) and 1972
(with Blyth and Janowitz’s book Residuation theory), a period containing fundamental
works like Öre’s 1944 paper Galois connexions or Croisot’s 1956 paper Applications
résiduées.