From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3679 Path: news.gmane.org!not-for-mail From: "Charles Wells" Newsgroups: gmane.science.mathematics.categories Subject: Re: Re: monic epics Date: Thu, 08 Mar 2007 10:13:09 -0500 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-1" X-Trace: ger.gmane.org 1241019451 9748 80.91.229.2 (29 Apr 2009 15:37:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:31 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Thu Mar 8 17:01:59 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 Mar 2007 17:01:59 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HPPaR-0001uJ-MQ for categories-list@mta.ca; Thu, 08 Mar 2007 16:51:43 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 33 Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:3679 Archived-At: It seems to me that Isbell's notion of "dominions" are something like a precise way of saying "a complete set of generators" for the case of epimorphisms in Cat. Look at "Epimorphisms and Dominions III" by John Isbell, American Journal of Mathematics, 1968. That paper has references to earlier papers about the case for semigroups and other categories. Charles Wells > ok i got it. in all the examples given the subobjects given by the > monics are "generators" for the object, where by "generators" i mean the > elements of the subobject in some way determine the elements of the > bigger object. so how about this then: any time we have the situation > described above the monic arrow will also be epic. > > -- Charles Wells abstract math website: http://www.abstractmath.org/MM//MMIntro.htm professional website: http://www.cwru.edu/artsci/math/wells/home.html personal website: http://www.abstractmath.org/Personal/index.html genealogical website: http://familytreemaker.genealogy.com/users/w/e/l/Charles-Wells/ NE Ohio Sacred Harp website: http://www.abstractmath.org/fasola/index.html