Jean Benabou

Jean Benabou

[Francis Borceux]

I heard with great sadness the death of Jean Benabou, from whom I learned a  lot.

Andree Ehresmann would like to publish some pages in the "Cahiers" in April, to sketch the career and the work of Jean Benabou.

Jean was somebody who liked very much teaching his ideas through beautiful talks ... but he was very reluctant to write papers.
Therefore, much of his work is known only through his talks and  some corresponding internal publications, written in general by some of his auditors,  in the universities where Jean taught.
If some of you have references of such publications, Andree and I would appreciate to know them in order to mention them in the "Cahiers".

Thank you in advance.

Francis Borceux
6 rue François
1490 Court-Saint-Etienne
+3210614205
+32478390328
francis.borceux@uclouvain.be



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Jean Benabou

[George Janelidze]

Jean Benabou was a great mathematician of our time.

He could criticize, and criticizing he could exaggerate, but if I had to sa=
y
a only few words describing him, I would choose:

Outstanding mathematical talent, honesty, and kindness.

George


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Jean Benabou

[Joyal, André]

I find it sad that Jean Benabou died a few days ago.

Benabou studied mathematics in Paris, but he was originally from Morocco.
He studied with Charles Ehresmann, but was deeply influenced by Grothendieck and his school.
He is well known for his fundamental contributions to category theory.
For many years, his seminar had an important role in the developpement and diffusion of category theory in Paris.
I will list some of his main contributions.

He was a pionner in the theory of monoidal categories, monoidal functors and related matters (1963)
He introduced bicategories and distributors (1967).
https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/DiWo.pdf
With Jacques Roubeau, he connected Grothendieck theory of descent  to Beck theory of monads (1970)
With William Mitchell, he formally connected intuitionistic set theory to the theory of elementary topoi (1972).
He used fibered categories for a general theory of parametrised categories
and also for the foundation of category theory and of logic (2014).

Jean had strong opinion about mathematics and category theory.
Like Grothendieck, he valued definitions as much as theorems.
He always wanted to dig deep into a matter, find a good terminology.
His mathematics was very elegant.
The last time I saw him in Paris he was developping
a notion of folliation for categories that was extending the notion of fibration.
I dont know if it was published.

André



https://gallica.bnf.fr/ark:/12148/bpt6k3208j/f1965.image
[https://gallica.bnf.fr/ark:/12148/bpt6k3208j/f1965.medres]<https://gallica.bnf.fr/ark:/12148/bpt6k3208j/f1965.image>
Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels | 1963-01 | Gallica<https://gallica.bnf.fr/ark:/12148/bpt6k3208j/f1965.image>
Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels -- 1963-01 -- fascicules
gallica.bnf.fr
https://link.springer.com/chapter/10.1007/BFb0074299
[https://static-content.springer.com/cover/book/978-3-540-35545-8.jpg]<https://link.springer.com/chapter/10.1007/BFb0074299>
Introduction to bicategories | SpringerLink<https://link.springer.com/chapter/10.1007/BFb0074299>
Cite this paper as: Bénabou J. (1967) Introduction to bicategories. In: Reports of the Midwest Category Seminar. Lecture Notes in Mathematics, vol 47.
link.springer.com
https://ncatlab.org/nlab/show/Benabou-Roubaud%20theorem

https://ncatlab.org/nlab/show/Mitchell-B%C3%A9nabou+language
Mitchell-Bénabou language<https://ncatlab.org/nlab/show/Mitchell-B%C3%A9nabou+language>
Context Topos Theory. topos theory. Toposes; Background. category theory. category. functor. Toposes (0,1)-topos, Heyting algebra, locale. pretopos
ncatlab.org

Fibrations petites et localement petites
https://gallica.bnf.fr/ark:/12148/bpt6k6228235m/f171.image

Fibered categories and the foundation of naive category theory

https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/fibered-categories-and-the-foundations-of-naive-category-theory/5BE99DB6F7BAE699D81D27BC5C0A3D80
[https://static.cambridge.org/covers/JSL_0_0_0/the_journal%20of%20symbolic%20logic.jpg?send-full-size-image=true]<https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/fibered-categories-and-the-foundations-of-naive-category-theory/5BE99DB6F7BAE699D81D27BC5C0A3D80>
Fibered categories and the foundations of naive category theory | The Journal of Symbolic Logic | Cambridge Core<https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/fibered-categories-and-the-foundations-of-naive-category-theory/5BE99DB6F7BAE699D81D27BC5C0A3D80>
Fibered categories and the foundations of naive category theory - Volume 50  Issue 1
www.cambridge.org
Théories relatives à un corpus:


https://gallica.bnf.fr/ark:/12148/bpt6k6228235m/f105.item


https://ncatlab.org/nlab/show/B%C3%A9nabou%20cosmos

https://fr.wikipedia.org/wiki/Cosmos_(th%C3%A9orie_des_cat%C3%A9gories)


https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/DiWo.pdf
Distributors at Work<https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/DiWo.pdf>
If Gis full and faithful then G#G(A) ’A#Aand, therefore, A is an isomorphism. Of course, L G preserves all colimits as it is a left adjoint. However, in general L G(F) does not have any particular good preservation properties as can be seen when considering Kan extension along id
www2.mathematik.tu-darmstadt.de


Cosmos (théorie des catégories) — Wikipédia<https://fr.wikipedia.org/wiki/Cosmos_(th%C3%A9orie_des_cat%C3%A9gories)>
En mathématiques, et plus spécifiquement en théorie des catégories,  un cosmos (au pluriel cosmoi) est une catégorie monoïdale symétrique  fermée qui est bicomplète [1].La notion a été introduite dans les années 1970 et est attribuée au mathématicien français Jean Bénabou [1], [2], [3].Elle généralise en un sens la construction d'un topos (qui est un modèle pour une théorie ...
fr.wikipedia.org




[For admin and other information see: http://www.mta.ca/~cat-dist/ ]