From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5561 Path: news.gmane.org!not-for-mail From: Steve Lack Newsgroups: gmane.science.mathematics.categories Subject: Re: Question on terminology Date: Sat, 06 Feb 2010 11:21:58 +1100 Message-ID: References: Reply-To: Steve Lack NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1265463212 28020 80.91.229.12 (6 Feb 2010 13:33:32 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 6 Feb 2010 13:33:32 +0000 (UTC) To: lamarche , categories Original-X-From: categories@mta.ca Sat Feb 06 14:33:29 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 1Ndkmu-0003B4-Sx for gsmc-categories@m.gmane.org; Sat, 06 Feb 2010 14:33:29 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NdkHO-0001ox-5j for categories-list@mta.ca; Sat, 06 Feb 2010 09:00:54 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5561 Archived-At: I would suggest "cancellative categories" - I believe the corresponding ter= m "cancellative monoid" is standard. Steve Lack. On 5/02/10 4:39 AM, "lamarche" wrote: >=20 > Is there a standard accepted name for categories all whose morphisms > are both epi and mono? This includes groupoids, posets and preorders, > along with free categories (from graphs), so it's not a trivial class > at all. >=20 > I am leaning towards calling them "integral categories", by analogy > with integral domains, but Google searches have been frustrating. > Another possiblility would be "cancellation categories" (they have > both the left and right cancellation property), but I'm not sure I > like this one. >=20 > Is there anything about these in the literature already? >=20 > Thanks in advance, >=20 > Fran=E7ois >=20 >=20 >=20 >=20 >=20 >=20 >=20 > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]