From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4610 Path: news.gmane.org!not-for-mail From: "Zinovy Diskin" Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Fri, 19 Sep 2008 18:21:14 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241020056 14034 80.91.229.2 (29 Apr 2009 15:47:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:36 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Sep 20 10:14:54 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 20 Sep 2008 10:14:54 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Kh2DR-0006SN-GV for categories-list@mta.ca; Sat, 20 Sep 2008 10:09:37 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 80 Original-Lines: 30 Xref: news.gmane.org gmane.science.mathematics.categories:4610 Archived-At: Dear Michael, Still some content in Steve's claim could be imagined. A working mathematician (WM) works with Borubaki's structures like groups or vector spaces and leaves all worries about what his proofs actually mean for a working math logician. For such a WM, sketches (as any other syntactical machineries) are indeed technical minutiae rather than mathematical objects. It'd be perhaps a reasonable view unless a bunch of strong semantic results (Tarski, Mal'cev,Robinson) that our WM values so much, which are provided by bringing syntax onto the stage. Zinovy On Thu, Sep 18, 2008 at 10:31 AM, Michael Barr wrote: > Of course sketches are mathematical objects in their own right. Of > course, the functor that assigns to each sketch the corresponding theory > is not full or faithful. But the definition is precise, the notion of > model is also precise, so I have no idea what, if any, content there is in > the claim. Incidentally, you might with equal justice claim that triples > are not mathematical objects since two distinct triples can have > isomorphic categories of Eilenberg-Moore algebras. In fact there are > triples (or theories) on Set that have infinitary operations, yet whose > category of models is isomorphic to Set. > > Michael >