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 we now call monoidal categories.

• JEAN BÉNABOU (1932–2022): The man and the mathematician, a biographical and mathematical sketch of Bénabou written by Francis Borceux, published in Cahiers de Topologie et Géométrie Différentielle Catégoriques, volume LXIII-3, 2022

Selected writings

Introducing the notion of enriched categories:

• Jean Bénabou, Catégories relatives, C. R. Acad. Sci. Paris, 260 (1965), pp. 3824-3827 (gallica)

On bicategories

• Jean Bénabou, Introduction to Bicategories, Lecture Notes in Mathematics 47, Springer (1967), pp.1-77. (doi)

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

• Jean Bénabou, Jacques Roubaud, Monades et descente, C. R. Acad. Sc. Paris, Ser. A 270 (1970) 96-98 [gallica:12148/bpt6k480298g/f100, pdf, English translation (by Peter Heinig): MO:q/279152]

On profunctors (including for enriched categories 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:

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

• Jean Bénabou, Fibered Categories and the Foundations of Naive Category Theory, The Journal of Symbolic Logic, Vol. 50, No. 1 (Mar., 1985), pp. 10-37 (doi)

See also:

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

Related $n$Lab entries

• bicategory

• Bénabou-Roubaud theorem

• internal language of a topos

  (Mitchell-Bénabou language)

• distributor

• Grothendieck fibration

• Bénabou cosmos

• foliated category

• displayed category

category: people