From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10660 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: =?Windows-1252?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Jean Benabou Date: Sun, 13 Feb 2022 20:23:20 +0000 Message-ID: Reply-To: =?Windows-1252?Q?Joyal=2C_Andr=E9?= Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="31588"; mail-complaints-to="usenet@ciao.gmane.io" To: "categories@mta.ca" Original-X-From: majordomo@rr.mta.ca Mon Feb 14 03:06:15 2022 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.75]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1nJQko-0007zT-TG for gsmc-categories@m.gmane-mx.org; Mon, 14 Feb 2022 03:06:15 +0100 Original-Received: from rr.mta.ca ([198.164.44.159]:44512) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1nJQhg-0000kF-1d; Sun, 13 Feb 2022 22:03:00 -0400 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1nJQhh-0000Db-TX for categories-list@rr.mta.ca; Sun, 13 Feb 2022 22:03:01 -0400 Accept-Language: fr-CA, en-US Content-Language: fr-CA Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10660 Archived-At: 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 Grothendiec= k 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 an= d 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 t= he 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 fibr= ation. I dont know if it was published. Andr=E9 https://gallica.bnf.fr/ark:/12148/bpt6k3208j/f1965.image [https://gallica.bnf.fr/ark:/12148/bpt6k3208j/f1965.medres] Comptes rendus hebdomadaires des s=E9ances de l'Acad=E9mie des sciences / p= ubli=E9s... par MM. les secr=E9taires perp=E9tuels | 1963-01 | Gallica Comptes rendus hebdomadaires des s=E9ances de l'Acad=E9mie des sciences / p= ubli=E9s... par MM. les secr=E9taires perp=E9tuels -- 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] Introduction to bicategories | SpringerLink Cite this paper as: B=E9nabou J. (1967) Introduction to bicategories. In: R= eports of the Midwest Category Seminar. Lecture Notes in Mathematics, vol 4= 7. link.springer.com https://ncatlab.org/nlab/show/Benabou-Roubaud%20theorem https://ncatlab.org/nlab/show/Mitchell-B%C3%A9nabou+language Mitchell-B=E9nabou language Context Topos Theory. topos theory. Toposes; Background. category theory. c= ategory. 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/a= bs/fibered-categories-and-the-foundations-of-naive-category-theory/5BE99DB6= F7BAE699D81D27BC5C0A3D80 [https://static.cambridge.org/covers/JSL_0_0_0/the_journal%20of%20symbolic%= 20logic.jpg?send-full-size-image=3Dtrue] Fibered categories and the foundations of naive category theory | The Journ= al of Symbolic Logic | Cambridge Core Fibered categories and the foundations of naive category theory - Volume 50= Issue 1 www.cambridge.org Th=E9ories relatives =E0 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 If Gis full and faithful then G#G(A) =92A#Aand, therefore, A is an isomorph= ism. 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 properti= es as can be seen when considering Kan extension along id www2.mathematik.tu-darmstadt.de Cosmos (th=E9orie des cat=E9gories) =97 Wikip=E9dia En math=E9matiques, et plus sp=E9cifiquement en th=E9orie des cat=E9gories,= un cosmos (au pluriel cosmoi) est une cat=E9gorie mono=EFdale sym=E9trique= ferm=E9e qui est bicompl=E8te [1].La notion a =E9t=E9 introduite dans les = ann=E9es 1970 et est attribu=E9e au math=E9maticien fran=E7ais Jean B=E9nab= ou [1], [2], [3].Elle g=E9n=E9ralise en un sens la construction d'un topos = (qui est un mod=E8le pour une th=E9orie ... fr.wikipedia.org [For admin and other information see: http://www.mta.ca/~cat-dist/ ]