From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6445 Path: news.gmane.org!not-for-mail From: "Reinhard Boerger" Newsgroups: gmane.science.mathematics.categories Subject: Re: source, sinks, and ? Date: Tue, 4 Jan 2011 11:44:01 +0100 Message-ID: Reply-To: "Reinhard Boerger" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1294150267 13133 80.91.229.12 (4 Jan 2011 14:11:07 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 4 Jan 2011 14:11:07 +0000 (UTC) Cc: To: "'Michael Shulman'" Original-X-From: majordomo@mlist.mta.ca Tue Jan 04 15:11:01 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 1Pa7bJ-0007is-FB for gsmc-categories@m.gmane.org; Tue, 04 Jan 2011 15:11:01 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:39013) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Pa7b9-0003El-Oh; Tue, 04 Jan 2011 10:10:51 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Pa7b4-0006BJ-Rk for categories-list@mlist.mta.ca; Tue, 04 Jan 2011 10:10:47 -0400 Thread-Index: Acuq2z0cVv/dOGmoQiOXhbnD+0w6XwBHaRUg Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6445 Archived-At: Hello, I am used to a slightly different terminology, which seems appropriate. > 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". For a sink, as I know it, the codomain should also be specified, i.e. a = sink is given by an object y and a family of morphisms x_i --> y. If I is not empty, this does not matter, but for empty I at least y should be given. = A cocone is given by an object y and a natural transformation from some functor to the constant functor with value y; her y is also specified. = So a sink is essentially a discrete cocone. A family { > x --> y_j }_{j \in J} all with the same domain is called a "source" or > a "cone".=20 These are the dual notions. > 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)? I do not know. Where does it occur? Probably the domain and codomain = should also be specified, possibly even an arrow. If a non-empty collection of arrows behave similarly (e.g. is mapped to the same arrow by a given = functor F), this means the same a saying that they all behave in the same way as = a given arrow 8e.g are mapped to some special morphism by F). A collection = of two objects x,y (prescribed domain and codomain) is something different; = it does not give an arrow Fx -->Fy. Greetings Reinhard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]