From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2760 Path: news.gmane.org!not-for-mail From: Robin Houston Newsgroups: gmane.science.mathematics.categories Subject: Proof nets Date: Mon, 19 Jul 2004 13:05:33 +0100 Message-ID: <20040719120533.GC26804@rpc142.cs.man.ac.uk> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241018887 5694 80.91.229.2 (29 Apr 2009 15:28:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:28:07 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jul 20 18:57:45 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 20 Jul 2004 18:57:45 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Bn2YR-0000Dn-00 for categories-list@mta.ca; Tue, 20 Jul 2004 18:53:43 -0300 Content-Disposition: inline User-Agent: Mutt/1.4i X-Spam-Score: -4.9 (----) X-Scanner: exiscan for exim4 (http://duncanthrax.net/exiscan/) *1BmWth-0005je-Hl*ERrT.CvyFHs* Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 24 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:2760 Archived-At: Dear categorists, The category of ordinary MLL proof nets (where an object is a term, and a morphism X -> Y is a cut-free proof net for |- X^, Y) is the free unitless *-autonomous category generated by the literals. Does the corresponding result hold for MALL? The Hughes-van Glabeek notion of MALL proof net has the ring of truth about it, and indeed they claim to have proven (theorem 4.22) that "two cut-free MALL proofs translate to the same proof net iff they can be converted into each other by a series of rule commutations". Of course the category of MALL proof nets is a unitless *-autonomous category with binary products and coproducts, but nowhere (to my knowledge) is it described as the *free* such category. Is that because it isn't, or merely because it isn't (yet) known to be? Enlightenment will be much appreciated. Yours, Robin