From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8630 Path: news.gmane.org!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: 2-cells in bicategories as bivectors Date: Sat, 6 Jun 2015 19:01:52 -0700 Message-ID: Reply-To: Mike Stay NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1433766442 14607 80.91.229.3 (8 Jun 2015 12:27:22 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 8 Jun 2015 12:27:22 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Mon Jun 08 14:27:13 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Z1w91-0000eY-UL for gsmc-categories@m.gmane.org; Mon, 08 Jun 2015 14:27:12 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58528) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Z1w7k-000709-95; Mon, 08 Jun 2015 09:25:52 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Z1w7i-00054l-F9 for categories-list@mlist.mta.ca; Mon, 08 Jun 2015 09:25:50 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8630 Archived-At: The "pentagonator" for the tensor product in a monoidal bicategory has edges that are all equivalences. There's a six-sided version of the pentagonator that goes from the identity on ((AB)C)D to the composition of five associators: ((AB)C)D -> ((AB)C)D || V ((AB)C)D -> (AB)(CD) -> A(B(CD)) -> A((BC)D) -> (A(BC))D -> ((AB)C)D Has anyone treated the pentagonator as having five edges that all run counterclockwise, and composition involves something like Stokes' theorem or bound current, where oppositely directed edges cancel out? 2-cells as bivectors? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]