From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2097 Path: news.gmane.org!not-for-mail From: maxk@maths.usyd.edu.au (Max Kelly) Newsgroups: gmane.science.mathematics.categories Subject: Re: 2-category of internal categories Date: Mon, 13 Jan 2003 20:02:45 -0400 Message-ID: <200301120527.h0C5Ruq312044@milan.maths.usyd.edu.au> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018410 2474 80.91.229.2 (29 Apr 2009 15:20:10 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:10 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Jan 13 20:09:53 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 13 Jan 2003 20:09:53 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18YEXV-0002Zp-00 for categories-list@mta.ca; Mon, 13 Jan 2003 20:02:45 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 22 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:2097 Archived-At: John Baez asks who constructed internal categories, functors, and natural transformations, proving these to form a 2-category; and seeks a reference. The answer is surely Ehresmann; and the precise reference must be in an early part of his collected works, produced after his death, with a detailed commentary, by his widow Andree Ehresmann-Bastiani. I have at least the earlier volumes of these, which - being now a visitor here in Sydney, John - you may certainly borrow. I'll have a bit of a look myself, if I have the time; Ehresmann's language is at times far from what has now become the norm. (Finding his categorical insights into differential geometry unappreciated by his French colleagues, he cut himself off and set up an independent group based in Paris VI (where he was) and in Amiens (where Bastiani was); with their own journal, Cahiers de Topologie et Geometrie Differentialle. The definitive rapprochement between this group and other category theorists dates from 1973, when the first of several international conferences at Amiens was arranged by Ehresmann and Bastiani.) Probably there will be no need for me to take these volumes down tonight; for Andree will doubtless see John's question when it dawns in Paris in an hour or two, and will doubtless give us chapter and verse. Max Kelly.