From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7200 Path: news.gmane.org!not-for-mail From: Robin Houston Newsgroups: gmane.science.mathematics.categories Subject: Re: Pullbacks of a family of arrows Date: Thu, 9 Feb 2012 15:02:17 +0000 Message-ID: References: Reply-To: Robin Houston NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (1.0) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1328820250 31092 80.91.229.3 (9 Feb 2012 20:44:10 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 9 Feb 2012 20:44:10 +0000 (UTC) Cc: Categories List To: Ohad Kammar Original-X-From: majordomo@mlist.mta.ca Thu Feb 09 21:44:09 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Rvaqf-0003SW-In for gsmc-categories@m.gmane.org; Thu, 09 Feb 2012 21:44:09 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:57824) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1RvapL-0008Jy-45; Thu, 09 Feb 2012 16:42:47 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RvapL-00075F-5x for categories-list@mlist.mta.ca; Thu, 09 Feb 2012 16:42:47 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7200 Archived-At: Wide pullback or fibre product, I think. Sent from my telephone On 8 Feb 2012, at 20:29, Ohad Kammar wrote: > What is the standard name for the limit of the diagram consisting of a mor= phism > f : A --> C > and an I-indexed family of morphisms > g_i : B_i --> C > where I is a set? >=20 > This is a slight generalisation of pullbacks. I am really interested > in the terminology for the following notion: >=20 > A class of morphisms M is stable under such generalised pullbacks if, > for all such limiting cones > a : P --> A > b_i : P --> B_i > if g_i are all in M, then so is the morphism a : P --> A >=20 > (This is a slight generalisation of stability of M under pullbacks.) >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]