From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7420 Path: news.gmane.org!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Profunctors and spans of sets Date: Sat, 25 Aug 2012 08:19:06 -0700 Message-ID: Reply-To: Mike Stay NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1345941392 30774 80.91.229.3 (26 Aug 2012 00:36:32 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 26 Aug 2012 00:36:32 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Sun Aug 26 02:36:31 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 1T5Qq6-0006mK-UL for gsmc-categories@m.gmane.org; Sun, 26 Aug 2012 02:36:31 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:57482) by smtpy.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1T5QpT-0005Jt-PI; Sat, 25 Aug 2012 21:35:51 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1T5Qpf-0004BL-Tw for categories-list@mlist.mta.ca; Sat, 25 Aug 2012 21:36:03 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7420 Archived-At: 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/ ]