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.
Francis Borceux: JEAN BÉNABOU (1932–2022): The man and the mathematician, Cahiers de Topologie et Géométrie Différentielle Catégoriques, LXIII-3 (2022) [pdf]
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):
Jean Bénabou, Catégories relatives, C. R. Acad. Sci. Paris, 260 (1965), pp. 3824-3827 (gallica)
Jean Bénabou, Structures algébriques dans les catégories, Cahiers de topologie et géométrie différentielle, 10 1 (1968) 1-126 [doi:CTGDC_1968__10_1_1_0]
On bicategories (and introducing the terminology monad):
On monadic descent via the Beck-Chevalley condition, the monadicity theorem and introducing the Bénabou-Roubaud theorem:
On monads:
On toposes:
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]
Jean Bénabou (notes by Thomas Streicher), Distributors at Work, lectures given at TU Darmstadt (2000) [pdf, pdf]
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:
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]
Scattered Notes on Benabouian Questions, recorded by Thomas Streicher
internal language of a topos
Last revised on March 3, 2025 at 19:09:37. See the history of this page for a list of all contributions to it.