From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7422 Path: news.gmane.org!not-for-mail From: Aleks Kissinger Newsgroups: gmane.science.mathematics.categories Subject: Re: Profunctors and spans of sets Date: Sun, 26 Aug 2012 17:37:29 +0100 Message-ID: References: Reply-To: Aleks Kissinger NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1346081746 31756 80.91.229.3 (27 Aug 2012 15:35:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 27 Aug 2012 15:35:46 +0000 (UTC) Cc: categories To: Mike Stay Original-X-From: majordomo@mlist.mta.ca Mon Aug 27 17:35:43 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1T61Kz-0001oQ-AP for gsmc-categories@m.gmane.org; Mon, 27 Aug 2012 17:34:49 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58904) by smtpy.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1T61KL-0005Ls-3R; Mon, 27 Aug 2012 12:34:09 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1T61Kb-0000XI-J6 for categories-list@mlist.mta.ca; Mon, 27 Aug 2012 12:34:25 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7422 Archived-At: I'm not sure about spans of spans, but the relationship between profunctors and spans (or cospans) of categories was pointed out by Benabou. I first saw this in a talk, which, fortuitously, Jeff Morton was also at, and wrote a blog post all about it: https://theoreticalatlas.wordpress.com/2011/05/18/benabou-spans-distributors/ a On 25 August 2012 16:19, Mike Stay wrote: > A span of sets X <-f- S -g-> Y can be viewed as a profunctor between > discrete categories by assigning to each pair (x,y) its preimage under > (f,g) o Delta. Similarly, a map of spans of sets can be seen as a > natural transformation between profunctors, while a span of spans of > sets can be seen as a profunctor between the corresponding collages. > > Where has this been discussed in the literature? > > In the bicategory of categories, profunctors, and natural > transformations, a profunctor from C to D with a right adjoint is (up > to some details around Cauchy completion) just a functor from C to D. > Is there a nice characterization of profunctors with right adjoints > when the 2-cells are profunctors between collages? > -- > 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/ ]