From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7138 Path: news.gmane.org!not-for-mail From: bourn@lmpa.univ-littoral.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: "Semi-additive" seems to be it Date: Mon, 9 Jan 2012 09:47:18 +0100 (CET) Message-ID: Reply-To: bourn@lmpa.univ-littoral.fr 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: dough.gmane.org 1326133292 4196 80.91.229.12 (9 Jan 2012 18:21:32 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 9 Jan 2012 18:21:32 +0000 (UTC) Cc: "Categories list" To: "George Janelidze" Original-X-From: majordomo@mlist.mta.ca Mon Jan 09 19:21:27 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 1RkJqZ-0003Qy-Cf for gsmc-categories@m.gmane.org; Mon, 09 Jan 2012 19:21:27 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:43864) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1RkJol-0007YR-Ha; Mon, 09 Jan 2012 14:19:35 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RkJol-0006bs-In for categories-list@mlist.mta.ca; Mon, 09 Jan 2012 14:19:35 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7138 Archived-At: 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 I agree with > May I try to protest against "plurality"? > > My reason of suggesting "half-" and not "semi-" is "semi-abelian". I understand that "semi-" is suggested by "semigroup", but "semi-abelian" was > suggested by "semidirect products". Note that "semidirect products" are defined categorically and a semi-abelian category is abelian if and only if > its semidirect products coincide with direct (that is, cartesian) produ= cts. > > Similarly, if a category with finite coproducts merely has semidirect products, then it is additive if and only if its semidirect products coincide with direct products. > > Another reason against > > "semi-additive =3D enriched in commutative monoids + has finite product= s" > > is that we do not want to identify monoids with semigroups, do we? > > And, surely, instead of saying that > > "While the category of commutative monoids is a motivating example of a semi-additive category, the category of commutative semigroups is not semi-additive" > > it is much better to say that > > "Semi- refers to semidirect products and not to semigroups". > > I hope to get support even from those who already made the opposite suggestion... > > George > > P.S. Well, I always try to respect old terminology, but sometimes (what= can > we do?) it is better to change it. By the way, many years ago Dmitrii Raikov > introduced another notion of "semi-abelian". As it turned out with help of > Yaroslav Kopylov, that Raikov semi-abelian means > > additive + regular + coregular > > It is an important notion with interesting examples, but what we call semi-abelian today seemed to be so much more suitable to call > "semi-abelian"! > > > -------------------------------------------------- > From: "Michael Barr" > Sent: Saturday, January 07, 2012 2:38 PM > To: "Categories list" > Subject: categories: "Semi-additive" seems to be it > >> Thanks for all the replies, but while there was consensus, >> "semi-additive" >> got a plurality and we will go with that. >> Michael >> -- >> Any society that would give up a little liberty to gain a little security will deserve neither and lose both. >> Benjamin Franklin >> [For admin and other information see: http://www.mta.ca/~cat-dist/ ] > > > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]