From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2910 Path: news.gmane.org!not-for-mail From: Joachim Kock Newsgroups: gmane.science.mathematics.categories Subject: Re: Semigroups with many objects Date: Fri, 25 Nov 2005 22:24:37 +0100 Message-ID: References: <281.4f1b3b.30b73c65@aol.com> 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 1241018979 6330 80.91.229.2 (29 Apr 2009 15:29:39 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:39 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sun Nov 27 21:02:15 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 27 Nov 2005 21:02:15 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EgXG0-0007jM-HX for categories-list@mta.ca; Sun, 27 Nov 2005 20:52:36 -0400 In-reply-to: <281.4f1b3b.30b73c65@aol.com> X-Sender: kock@127.0.0.1:55110 X-Spam-Checker-Version: SpamAssassin 3.0.4 (2005-06-05) on mx1.mta.ca X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.0.4 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 55 Original-Lines: 42 Xref: news.gmane.org gmane.science.mathematics.categories:2910 Archived-At: >Is there an accepted terminology for semigroups with many objects, i= .e. >gadgets that satisfy the all the axioms satisfied by categories exce= pting those which refer to identities ? Perhaps 'semi-category' is the most widely used term.=20 The word 'taxonomy' has also been used (Par=E9, Wood, Ageron), but Koslowski has used that word for something a bit more complicated ('interpolads in SPAN'). On the other hand, Schroeder has used the word 'semi-category' for the 'multiplicative graphs' of Ehresmann (some structure where composition of arrows is not always defined even if their source and target match). (Curiously, in a preliminary version of the paper by Moens, Berni-Canani, and Borceux, 'On regular presheaves and regular semi-categories', the term 'multiplicative graph' was used for 'semi-category' -- the final version uses 'semi-category'.) I would also like to advogate 'semi-monoid' instead of 'semi-group', and 'semi-monoidal category' for 'monoidal category without unit'. It seems to be too late at this point to convince operadists to say 'semi-operad' for operads without unit. In the same spirit I find it convenient to use 'semi-simplicial set' for presheaves on Delta-mono, but I am told that this is confusing, since apparently 'semi-simplicial set' meant something else fifty years ago... Cheers, Joachim. ---------------------------------------------------------------- Joachim Kock Departament de Matem=E0tiques -- Universitat Aut=F2noma de Barcelona Edifici C -- 08193 Bellaterra (Barcelona) -- ESPANYA Phone: +34 93 581 25 34 Fax: +34 93 581 27 90 ----------------------------------------------------------------