From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4598 Path: news.gmane.org!not-for-mail From: Andre.Rodin@ens.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Wed, 17 Sep 2008 06:36:49 +0200 Message-ID: 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 1241020049 13989 80.91.229.2 (29 Apr 2009 15:47:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:29 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Sep 18 10:34:48 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 18 Sep 2008 10:34:48 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KgJZF-0005e2-Vt for categories-list@mta.ca; Thu, 18 Sep 2008 10:29:10 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 68 Original-Lines: 36 Xref: news.gmane.org gmane.science.mathematics.categories:4598 Archived-At: Dear Steve, > Sketches are not mathematical objects in their own right, in the same s= ense > that groups or spaces are. Of course, they are not. >They are presentations (for theories), and have > status similar to other sorts of presentations (for groups, rings, etc.= ) I think about a sketch as an alternative to a string of formulae, which represents (axioms of) a theory. I didn't try to compare sketch theory wi= th group theory. I tried to compare sketch theory with the general setting,= in which group theory is developed a la Bourbaki (along with many other theories). A classical account of this general setting (which differs at = certain points with Bourbaki's version) is Tarski's model theory. The notion of presentation in my understanding implies that what a given presentation is a presentation *of* is somehow given in advance. I try to= think of a sketch as a means to build a theory, not to present a ready-made the= ory. Perhaps *representation* is a better word for it than *presentation*. best, andrei