From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4320 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: The Category of Semimodules over Semirings Date: Sun, 16 Mar 2008 13:43:24 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019870 12745 80.91.229.2 (29 Apr 2009 15:44:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:44:30 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Sun Mar 16 21:56:30 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 16 Mar 2008 21:56:30 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Jb3ag-0005vj-8i for categories-list@mta.ca; Sun, 16 Mar 2008 21:52:38 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 84 Original-Lines: 31 Xref: news.gmane.org gmane.science.mathematics.categories:4320 Archived-At: On Sun, 16 Mar 2008 09:26:35 AM EDT Jawad Abuhlail = wrote, in part, on the Subject: The Category of Semimodules over Semiring= s, > ... The category of semimodules had products, equalizers and > products (however not necessarily coequalizers). = I must be missing something here. Don't the (say, left-) semimodules (over a given semiring) constitute an equationally definable class = of algebras? That is, aren't they determined entirely by operations = and equations? If they DO, that is, if they ARE, then the category of them all (together= with their homomorphisms) must, like all such "varietal categories," have= = all (small) limits and colimits, and, in particular, all coequalizers. Alas, I have little else to offer. Cheers, and Happy St. Paddy's Day, -- Fred