From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8249 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: RE: A brief survey of cartesian functors Date: Mon, 28 Jul 2014 15:53:00 +0000 Message-ID: References: Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1406682030 27490 80.91.229.3 (30 Jul 2014 01:00:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 30 Jul 2014 01:00:30 +0000 (UTC) To: =?iso-8859-1?Q?Jean_B=E9nabou?= , Categories Original-X-From: majordomo@mlist.mta.ca Wed Jul 30 03:00:23 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XCIFi-0004OT-DP for gsmc-categories@m.gmane.org; Wed, 30 Jul 2014 03:00:22 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:49054) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XCIFQ-0004DG-22; Tue, 29 Jul 2014 22:00:04 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XCIFQ-0007ma-IO for categories-list@mlist.mta.ca; Tue, 29 Jul 2014 22:00:04 -0300 In-Reply-To: Accept-Language: en-US, en-CA Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8249 Archived-At: Dear Jean,=0A= =0A= I apologise for my ignorance of your work.=0A= =0A= I guess that an equivalence of categories P:X-->S is always a foliation, bu= t not=0A= a fibration, unless it is surjective on objects.=0A= =0A= -Andr=E9=0A= =0A= __________________________________=0A= From: Jean B=E9nabou [jean.benabou@wanadoo.fr]=0A= Sent: Monday, July 28, 2014 5:54 AM=0A= To: Categories=0A= Subject: categories: A brief survey of cartesian functors=0A= =0A= Dear Ross, Dear all,=0A= =0A= In a recent mail I asked Ross if pseudo cartesian functors between pseudo f= ibrations had been studied.=0A= There are many generalizations of fibrations. Pseudo fibrations are only on= e of them. But there are also prefibrations, defined by Grothendieck, but a= lmost never considered, and pre foliations, which I define here, which gen= eralise greatly pre fibrations. For such pre foliatons, I define cartesian = functors and show that they have striking properties, most of which are no= t known, even in the very special case of fibrations.=0A= I thought this brief survey might interest you, in case you decide to study= seriously the properties of pseudo cartesian functors.=0A= =0A= Best regards to all,=0A= Jean=0A= =0A= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]