From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1570 Path: news.gmane.org!not-for-mail From: Andree Ehresmann Newsgroups: gmane.science.mathematics.categories Subject: Answer to Charles Wells Date: Wed, 12 Jul 2000 18:45:46 +0200 Message-ID: <3.0.3.32.20000712184546.006983ac@mailx.u-picardie.fr> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1241017932 31870 80.91.229.2 (29 Apr 2009 15:12:12 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:12:12 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Jul 13 10:18:26 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA10126 for categories-list; Thu, 13 Jul 2000 09:52:02 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: ehres@mailx.u-picardie.fr X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id NAA13402 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 12 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:1570 Archived-At: In answer to Charles Wells >Can anyone tell me what Ehresmann meant by a "saturated functor" >(foncteur saturé) in 1967? Charles Ehresmann defined a "homomorphism saturated functor" already in his lectures in 1962, and it figures in his 1963 paper "Categories structurees" (Annales ENS), reprinted in "Charles Ehresmann: Oeuvres completes et Commentees", Part III-1, Amiens 1980, p. 29 In the "Comments" in this book I have given English translations in more modern terms of the main categorical definitions and results of Charles, which, up to the seventies, were often written in a non-usual style, very difficult to decipher to-day (and even at that moment for most readers, which explains they were not as widely known as they should have been!) In particular in the Note 29-2 (p. 348-9 of this book) I have translated the definition in more modern terms: A "homomorphism saturated functor" p: H -> C is a faithful amnestic functor which creates isomorphisms; amnestic means that an isomorphism mapped on an identity is an identity. Thus H is a concrete category over C, such that the restriction of p to the groupoid of isomorphisms of H is a discrete op-fibration. (there are more information in this Note).