From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7380 Path: news.gmane.org!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Re: Examples of symmetric monoidal bicategories Date: Sat, 14 Jul 2012 11:11:29 -0700 Message-ID: References: Reply-To: Mike Stay NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1342347044 17709 80.91.229.3 (15 Jul 2012 10:10:44 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 15 Jul 2012 10:10:44 +0000 (UTC) Cc: categories@mta.ca To: =?ISO-8859-1?Q?Roman_Krenick=FD?= Original-X-From: majordomo@mlist.mta.ca Sun Jul 15 12:10:44 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1SqLml-00071h-Q6 for gsmc-categories@m.gmane.org; Sun, 15 Jul 2012 12:10:43 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:56569) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SqLlq-0005CH-Ao; Sun, 15 Jul 2012 07:09:46 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SqLlp-0002a4-Tj for categories-list@mlist.mta.ca; Sun, 15 Jul 2012 07:09:45 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7380 Archived-At: On Thu, Jul 12, 2012 at 7:59 AM, Roman Krenick=FD wrote: > Dear all, > > I'm looking for examples of symmetric monoidal bicategories (where the > structure is genuinely weak, i.e. the various isomorphisms are not > identities) and I would appreciate some help. -- Actually, strict > 2-categories with (genuinely) weak monoidal structure would be even more > interesting, but I found it almost impossible to find anything on that. > > As I am using these categories as models, I need some structure that is > "concrete enough" to do calculations with (while being as simple as > possible). > > Right now I'm considering the bicategory of rings (or monoids or > fields), bimodules over them, and bimodule homomorphisms, where the > monoidal structure is defined by the tensor product etc. (Pointers to > detailed accounts of this category would be very much appreciated, too. > I've only found fairly sketchy mentions in the literature.) > > I would be grateful about any other examples of this kind! Spans of sets. The cartesian product of sets has an associator, so the tensor product of spans does, too. --=20 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/ ]