nLab Jean Bénabou

Jean Bénabou (1932-2022) was a French mathematician working in category theory. He studied under the supervision of Charles Ehresmann and received his Thèse d’État from the Université de Paris in 1966 on the topic of what are now called monoidal categories.

Selected writings

Introducing the notion of monoidal categories (then under the name “categories with multiplication” or “multiplicative categories”):

  • Jean Bénabou, Catégories avec multiplication , C. R. Acad. Sci. Paris 256 (1963) 1887-1890 [gallica]

  • Jean Bénabou, Algèbre élémentaire dans les catégories avec multiplication , C. R. Acad. Sci. Paris 258 (1964) 771-774 [gallica]

  • Jean Bénabou, Les catégories multiplicatives, Séminaire de mathématique pure 27, Université de Louvain (1972) [pdf]

Introducing the notion of enriched categories (and of strict 2-categories, as an example):

On bicategories (and introducing the terminology monad):

  • Jean Bénabou, Introduction to Bicategories, Lecture Notes in Mathematics 47 Springer (1967) 1-77 [doi:10.1007/BFb0074299]

On monadic descent via the Beck-Chevalley condition, the monadicity theorem and introducing the Bénabou-Roubaud theorem:

On monads:

  • Jean Bénabou, Les Triples, Séminaire de mathématiquepure pure 26, Université de Louvain (1972) [pdf]

On toposes:

  • Jean Bénabou, Problèmes dans les topos, Séminaire de mathématiquepure pure 34, Université de Louvain (1973) [pdf]

On profunctors (“distributors”, including for enriched and internal categories):

  • Jean Bénabou, Les distributeurs, Université Catholique de Louvain, Institut de Mathématique Pure et Appliquée, rapport 33 (1973) [pdf, pdf]

On fibered categories:

  • Jean Bénabou, Fibrations petites et localement petites, C. R. Acad. Sci. Paris 281 Série A (1975) 897-900 [gallica]

  • Jean Bénabou, Fibered Categories and the Foundations of Naive Category Theory, The Journal of Symbolic Logic, Vol. 50 1 (1985) 10-37 [doi:10.2307/2273784]

See also:

On foliated categories:

  • Jean Bénabou, Cartesian functors and foliated categories, talk at Oxford (1 May 2012) [YouTube]

  • Jean Bénabou, Foncteurs cartésiens et catégories feuilletées, talk at Journée Guitart, Paris (9 November 2012) [YouTube, slides, pdf]

  • Jean Bénabou, Du vieux et du neuf sur la construction de Grothendieck, talk at Paris-Diderot (March 2019) [YouTube]

    (the material on foliated categories – called simply foliations — starts at 1:01:00).

See also:

  • J. Bénabou, Théories relatives à un corpus, C. R. Acad. Sci. Paris 281 Série A (1975) 831-834. [gallica]
category: people

Last revised on January 22, 2024 at 07:22:54. See the history of this page for a list of all contributions to it.