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/ab... [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/ ]