From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6442 Path: news.gmane.org!not-for-mail From: burroni@math.jussieu.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: source, sinks, and ? Date: Mon, 03 Jan 2011 23:40:47 +0100 Message-ID: References: Reply-To: burroni@math.jussieu.fr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1294098634 1025 80.91.229.12 (3 Jan 2011 23:50:34 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 3 Jan 2011 23:50:34 +0000 (UTC) Cc: categories To: Michael Shulman Original-X-From: majordomo@mlist.mta.ca Tue Jan 04 00:50:30 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PZuAX-0005MA-Dd for gsmc-categories@m.gmane.org; Tue, 04 Jan 2011 00:50:29 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:47792) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PZuAB-0004ZZ-B5; Mon, 03 Jan 2011 19:50:07 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PZuA7-0003uq-OJ for categories-list@mlist.mta.ca; Mon, 03 Jan 2011 19:50:03 -0400 In-Reply-To: Content-Disposition: inline Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6442 Archived-At: Dear Mike, In fact, we can call it a matrix (of (I x J)- type) with coefficients =20 in the category. When the category is a category of modules, we have =20 that way a natural generalization of classical matrices. Cheers, Albert Michael Shulman a =E9crit=A0: > A family of morphisms { x_i --> y }_{i \in I} in some category, all > with the same codomain, is called a "sink" or a "cocone". A family { > x --> y_j }_{j \in J} all with the same domain is called a "source" or > a "cone". Is there a name for a family of the form { x_i --> y_j }_{i > \in I, j \in J} ? A cylinder? Or a frustrum (since I \neq J)? > > Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]