From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6391 Path: news.gmane.org!not-for-mail From: Alan Jeffrey Newsgroups: gmane.science.mathematics.categories Subject: Is "braided monoidal" a conservative extension of "lax braided monoidal"? Date: Mon, 29 Nov 2010 10:34:35 -0600 Message-ID: Reply-To: Alan Jeffrey NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-1"; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1291059077 17356 80.91.229.12 (29 Nov 2010 19:31:17 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 29 Nov 2010 19:31:17 +0000 (UTC) To: Original-X-From: majordomo@mlist.mta.ca Mon Nov 29 20:31:12 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PN9RP-0000o4-Lw for gsmc-categories@m.gmane.org; Mon, 29 Nov 2010 20:31:11 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59652) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PN9Qp-0002nP-Ik; Mon, 29 Nov 2010 15:30:35 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PN9Qk-0005Nc-TQ for categories-list@mlist.mta.ca; Mon, 29 Nov 2010 15:30:31 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6391 Archived-At: Hi everyone, Is there a known result (or counterexample) saying that the equational theory of a braided monoidal category is a conservative extension of a lax braided monoidal category? As a reminder, a lax braid is a natural b : A * B -> B * A satisfying coherence conditions with the units and associators, and a braid is a lax braid where b is an isomorphism. The motivation for asking this question is that string diagrams are a proof technique for braids, and I'd like to be able to use them for lax braids too, but this requires braiding to be a conservative extension of lax braiding. Cheers, Alan Jeffrey. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]