From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5558 Path: news.gmane.org!not-for-mail From: lamarche Newsgroups: gmane.science.mathematics.categories Subject: Question on terminology Date: Thu, 4 Feb 2010 18:39:32 +0100 Message-ID: Reply-To: lamarche NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=ISO-8859-1; format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1265416802 6576 80.91.229.12 (6 Feb 2010 00:40:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 6 Feb 2010 00:40:02 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Sat Feb 06 01:39:59 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1NdYiL-000862-2D for gsmc-categories@m.gmane.org; Sat, 06 Feb 2010 01:39:57 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NdY6y-0005St-Hw for categories-list@mta.ca; Fri, 05 Feb 2010 20:01:20 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5558 Archived-At: Is there a standard accepted name for categories all whose morphisms =20 are both epi and mono? This includes groupoids, posets and preorders, =20= along with free categories (from graphs), so it's not a trivial class =20= at all. I am leaning towards calling them "integral categories", by analogy =20 with integral domains, but Google searches have been frustrating. =20 Another possiblility would be "cancellation categories" (they have =20 both the left and right cancellation property), but I'm not sure I =20 like this one. Is there anything about these in the literature already? Thanks in advance, Fran=E7ois [For admin and other information see: http://www.mta.ca/~cat-dist/ ]