Jacques Riguet
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Jacques Riguet (1921 to October 20, 2013) was a French mathematician known for his contributions to algebraic logic and category theory. According to
Gunther Schmidt Gunther Schmidt (born 1939, Rüdersdorf) is a German mathematician who works also in informatics. Life Schmidt began studying Mathematics in 1957 at Göttingen University. His academic teachers were in particular Kurt Reidemeister, Wilhelm Kl ...
and Thomas Ströhlein, "
Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician a ...
and Jacques Riguet founded the modern
calculus of relations In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for ...
".


Career

Already at his lycée, Riguet was impressed by the power of geometric reasoning. He studied
Louis Couturat Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. Life and education Born in Ris-Orangis, Essonne, France. In 1887 he ...
and Bourbaki, who made contributions to logic and
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
.Stephane Dugowson and others
Hommage a Jacques Riguet
at
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Riguet studied higher mathematics with
Albert Châtelet Albert Châtelet (24 October 1883 – 30 June 1960) was a French politician and mathematician. Biography Châtelet was a student at the École normale supérieure (Paris) from 1905 to 1908, succeeding to the Agrégation (a highly selective compe ...
and was introduced to
lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an orna ...
s. In 1948 he published "Relations binaires, fermetures, correspondances de Galois" which revived the calculus of binary relations. He published his thesis ''Fondements de la Theorie de Relations Binaires'' in October 1951. In 1954 Riguet gave a plenary address at the International Congress of Mathematicians in Amsterdam, speaking on the applications of binary relations to algebra and machine theory. For a time, Riguet attended the seminary of Jacques Lacan. Riguet was employed at
Centre national de la recherche scientifique The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,63 ...
until 1957.


Relations

In Riguet's work the composition of relations is the basis for characterizing relations, replacing the element-wise descriptions that use logical formulations. For example, he described the Schröder rules. His work was reviewed in
Journal of Symbolic Logic The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by ''Mathematical Reviews'', Zentralb ...
by Øystein Ore. Some of Riguet’s contributions can be described using structure of the logical matrix associated with a relation. If ''u'' and ''v'' are logical vectors, then their logical outer product produces the associated logical matrix u_i \land v_j . Riguet calls the associated relation a rectangular relation, and if it happens to be symmetric it is a square relation. In 1950 he submitted "Sur les ensembles reguliers de relations binaires", and an article on difunctional relations, those with logical matrix in a
block diagonal In mathematics, a block matrix or a partitioned matrix is a matrix that is '' interpreted'' as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block matrix can be visualized as the original m ...
form. The following year he provided an algebraic characterization of
heterogeneous relation In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over sets and is a new set of ordered pairs consisting of elements in and in ...
s with a logical matrix comparable to a
Ferrers diagram In number theory and combinatorics, a partition of a positive integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same part ...
. Since Ferrers diagrams order the
partition Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...
of an integer, Riguet extended order theory beyond relations restricted to one set. In 1954 Riguet described the extension of the calculus of binary relations to a calculus of Boolean matrices.


Category theory

In 1958 Riguet went to Zurich, working with IBM , studying category theory. He published the following papers on that topic: * 1962: "Programmation et theorie des categories", in ''Proceedings of Symposium on Symbolic Languages and Data Processing'', Rome (1961), pp 88–98,
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* 1973: "Probabilites et theorie de la decision du point de vue de la theorie des categories" (Amiens colloquium) Cahiers de Topologie et Géométrie Différentielle Catégoriques 14(2) * 1975 : "Theorie des jeux et funciones de Grundy du point de vue de la theorie des categories" (TAC-Chantilly) ''Cahiers de Topologie et Géométrie Différentielle Catégoriques'' 16(4) : 441 * 1989 : "Galois correspondences in category theory", Hesselberg-Combinatorics * 1992: (with Rene Guitart
Enveloppe Karoubienne et categorie de Kleisli
''Cahiers de Topologie et Géométrie Différentielle Catégoriques'' 33(3) : 261–6, via Numdam.org Riguet participated in the Séminaire Itinérant des Catégories.Séminaire Itinérant des Catégories (16 November 2013
Hommage du SIC a Jacques Riguet
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References

{{DEFAULTSORT:Riguet, Jacques 1921 births 2013 deaths 20th-century French mathematicians Category theorists