From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5501 Path: news.gmane.org!not-for-mail From: burroni@math.jussieu.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: small is beautiful Date: Sat, 09 Jan 2010 22:05:24 +0100 Message-ID: References: Reply-To: burroni@math.jussieu.fr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1263149013 9977 80.91.229.12 (10 Jan 2010 18:43:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 10 Jan 2010 18:43:33 +0000 (UTC) To: Paul Taylor , Original-X-From: categories@mta.ca Sun Jan 10 19:43:26 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1NU2kg-0003pf-Uy for gsmc-categories@m.gmane.org; Sun, 10 Jan 2010 19:43:03 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NU2H1-0007mO-MY for categories-list@mta.ca; Sun, 10 Jan 2010 14:12:23 -0400 In-Reply-To: Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5501 Archived-At: Dear Paul, > (I believe that there was a development of "locally internal" instead of > "locally small" categories by some French categorists in the 1970s -- > Burroni again maybe?.) I must mention that it is not me, but Jacques Penon who has worked on =20 "locally internal" notions. I would like to add (to my yesterday mail) some indications on what I =20 have called "small categories theory". In fact, this theory begins to =20 exist. It is, for instance, what is called the "higher dimensionnal =20 words problem", but also a developpement on higher automata theory (I =20 have made many talks on this subjet, but not published --- I can send =20 a manuscript to anybody interested). I have for example proved that =20 finite and finitary Lawvere theory are finitely presentable 2-mono=EFds =20 (it is my motivation for introducing the notion of polygraphs, =20 previously introduced by Ross Street under the name of computads). It =20 is perhaps not well-known by the categorists because it is published =20 in a computer sciences revue : http://people.math.jussieu.fr/~burroni/mapage/highwordpb.pdf Best, Albert [For admin and other information see: http://www.mta.ca/~cat-dist/ ]