From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2734 Path: news.gmane.org!not-for-mail From: "Noson Yanofsky" Newsgroups: gmane.science.mathematics.categories Subject: Questions on dinatural transformations. Date: Tue, 29 Jun 2004 13:19:46 -0400 Message-ID: Reply-To: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018861 5537 80.91.229.2 (29 Apr 2009 15:27:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:27:41 +0000 (UTC) To: "categories@mta. ca" Original-X-From: rrosebru@mta.ca Wed Jun 30 18:29:16 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Jun 2004 18:29:16 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BfmZn-00016X-00 for categories-list@mta.ca; Wed, 30 Jun 2004 18:25:07 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 19 Original-Lines: 47 Xref: news.gmane.org gmane.science.mathematics.categories:2734 Archived-At: Hello, Two quick questions: a) It is well known that there is no vertical composition of dinatural transformations. How about horizontal composition? i.e. Given S,S':C^op x C---->B T,T':C^op x C ----> B^op U,U':B^op x B --->A \alpha: S--->S' dinat \alpha': T--->T' dinat and \beta: U--->U' dinat is there a \beta \circ (\alpha',\alpha) and is it dinat? It should be. But I can not seem to find the right definition. How about if we restrict to a nice category of moduals for a nice algebra over a nice field? Does that help? I was hoping that the category of small categories, functors and dinat transformations should be a graph-category (a category enriched over graphs) but am having a hard time finding what the composition is. Did someone write on these things? b) Also, I was wondering if anyone ever wrote about quasi-dinatural transformations. Those are dinats where the target category is a 2-category and the hexagon commutes up to a two cell. They show up in something I am working on. But they are very painful. Has anyone worked on such things? Any thoughts? All the best, Noson Yanofsky