From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7139 Path: news.gmane.org!not-for-mail From: Robin Cockett Newsgroups: gmane.science.mathematics.categories Subject: Re: "Semi-additive" seems to be it Date: Mon, 9 Jan 2012 12:39:33 -0700 Message-ID: References: Reply-To: Robin Cockett NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1326207332 18909 80.91.229.12 (10 Jan 2012 14:55:32 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 10 Jan 2012 14:55:32 +0000 (UTC) Cc: Categories list To: bourn@lmpa.univ-littoral.fr Original-X-From: majordomo@mlist.mta.ca Tue Jan 10 15:55:28 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 1Rkd6j-0005oz-Dq for gsmc-categories@m.gmane.org; Tue, 10 Jan 2012 15:55:25 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:50098) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Rkd5T-0005oI-RV; Tue, 10 Jan 2012 10:54:07 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Rkd5S-0004er-Lk for categories-list@mlist.mta.ca; Tue, 10 Jan 2012 10:54:06 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7139 Archived-At: Dear all, I completely agree with Dominique and George!!!! In response to Michael's posting I mentioned privately that Robert Seely, Rick Blute, and I (and others) had, in our work on differential categories, been using commutative monoid enriched categories and, to avoid this mouthful, had just called them "additive". Michael, as I expected did not like this at all as, of course, this means to him Abelian Group enriched. He did not like my suggestion "subtactive" as a replacement for Abelian Group enriched categories either :-) Just to mix things up: as our work is closely related to linear logic the direction of choosing "linear" was not attractive to us either: "linear" in that context means something different again! The stubborn fact is that there are only so many meaningful names. When one does a piece of work one wants to give snappy names to the important concepts in the work. Trying for a globally acceptable snappy name is almost impossible ... so I, for one, am happy to fall back on local naming conventions to replace more cumbersome formal names. And am not above poaching a name if I think it actually describes the concept well in that context. So the point is I am absolutely happy with "commutative monoid enriched category" as formal nomenclature and I am happy if an author wants to do some local naming to make things more readable. Of course, some choices are better than others! I am afraid I also shudder at semi-additive: it suggests commutative semigroup enrichment to me and relegates the concept to being a secondary one ... -robin (Robin Cockett) On Mon, Jan 9, 2012 at 1:47 AM, wrote: > Dear all, > > I completely agree with George. > > By the way, I studied such kind of categories (among others) in: > "Intrinsic centrality and associated classifying properties" > J. of Algebra, 256, 2002, 126-145. > I called them "linear", following Lawvere and Schanuel's "Conceptual > Mathematics". > > Truly yours, > > Dominique [For admin and other information see: http://www.mta.ca/~cat-dist/ ]