From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7142 Path: news.gmane.org!not-for-mail From: Todd Trimble Newsgroups: gmane.science.mathematics.categories Subject: Re: "Semi-additive" seems to be it Date: Tue, 10 Jan 2012 10:07:22 -0500 Message-ID: References: Reply-To: Todd Trimble NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 X-Trace: dough.gmane.org 1326288964 19958 80.91.229.12 (11 Jan 2012 13:36:04 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 11 Jan 2012 13:36:04 +0000 (UTC) Cc: Categories list To: Ross Street Original-X-From: majordomo@mlist.mta.ca Wed Jan 11 14:36:00 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RkyLO-0000hc-I3 for gsmc-categories@m.gmane.org; Wed, 11 Jan 2012 14:35:58 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:58713) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1RkyJx-0008L1-OU; Wed, 11 Jan 2012 09:34:29 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RkyJx-0003Ah-8v for categories-list@mlist.mta.ca; Wed, 11 Jan 2012 09:34:29 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7142 Archived-At: I also find "linear" an attractive option. Just to circumvent any confusion (e.g. with linear in the sense of linear logic, or with the question that may arise: linear over what?), one could say "N-linear" where N is of course the initial rig, as alluded to by Ross. I would hope that "N-linear category" is sufficiently unambiguous to get the meaning across, and sufficiently snappy. Best regards, Todd ----- Original Message ----- From: "Ross Street" To: Cc: "Categories list" Sent: Monday, January 09, 2012 9:35 PM Subject: categories: Re: "Semi-additive" seems to be it > Dear All > > The concept of category enriched in commutative monoids is a very > basic structure and it is important to find a suitable name. > I must say I like the term "linear" mentioned by Dominique since the > term "k-linear" is commonly used for "enriched in vector spaces over k". > Hence there is no conflict if we extend to the case where k is a ring > or a rig. > Since the natural numbers is the basic example of a rig, we can drop > the k in this case. > > Best wishes, > Ross > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]