From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7136 Path: news.gmane.org!not-for-mail From: "George Janelidze" Newsgroups: gmane.science.mathematics.categories Subject: Re: "Semi-additive" seems to be it Date: Sat, 7 Jan 2012 21:48:24 +0200 Message-ID: References: Reply-To: "George Janelidze" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed;charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1326037666 15391 80.91.229.12 (8 Jan 2012 15:47:46 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 8 Jan 2012 15:47:46 +0000 (UTC) To: "Michael Barr" , "Categories list" , Original-X-From: majordomo@mlist.mta.ca Sun Jan 08 16:47:42 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 1RjuyD-0008La-Tt for gsmc-categories@m.gmane.org; Sun, 08 Jan 2012 16:47:42 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42179) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1RjuwR-0001rT-C9; Sun, 08 Jan 2012 11:45:51 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RjuwR-0001II-2N for categories-list@mlist.mta.ca; Sun, 08 Jan 2012 11:45:51 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7136 Archived-At: 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) products. 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 = enriched in commutative monoids + has finite products" 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/ ]