From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3666 Path: news.gmane.org!not-for-mail From: Lawrence Stout Newsgroups: gmane.science.mathematics.categories Subject: Re: monic epics Date: Tue, 6 Mar 2007 21:41:21 -0600 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019444 9693 80.91.229.2 (29 Apr 2009 15:37:24 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:24 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Mar 7 13:54:30 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 Mar 2007 13:54:30 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HP0HA-0001Tg-FP for categories-list@mta.ca; Wed, 07 Mar 2007 13:50:08 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 20 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:3666 Archived-At: The Goguen category of L-fuzzy sets on a lattice L (Objects are pairs (A,\alpha) where \alpha:A\to L and morphisms are functions f:A\to B such that \beta{f(a)) >= \alpha(a)) has all functions whose underlying set function is an isomorphism both epic and monic, but not, in general, isomorphisms, which must preserve the lattice valued membership on the nose. Since these monic, epic maps are the ones which give the right subobjects to consider for fuzzy logic they are of interest. They do not determine a "folding" like the one you describe. On Mar 6, 2007, at 7:11 PM, David Karapetyan wrote: > So does every monic, epic arrow determine such a > "folding" or are there monic, epics that can't be characterized in > such > a way? > > Lawrence Stout Professof of Mathematics Illinois Wesleyan University