From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2383 Path: news.gmane.org!not-for-mail From: Jpdonaly@aol.com Newsgroups: gmane.science.mathematics.categories Subject: Correction to terminology (Pat Donaly) Date: Tue, 8 Jul 2003 15:55:25 EDT Message-ID: <116.25e2326c.2c3c7bad@aol.com> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018617 3857 80.91.229.2 (29 Apr 2009 15:23:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:23:37 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Jul 9 11:12:43 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 09 Jul 2003 11:12:43 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19aFcI-00045s-00 for categories-list@mta.ca; Wed, 09 Jul 2003 11:08:18 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 11 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:2383 Archived-At: Jean Pradines has kindly corrected my usage of "intertwining function". I erred in attempting to extend this term to the variant naturality concept described but not named by Mac Lane in problem 5, page 19 of either edition of "Categories for the Working Mathematician". To within order of the functors which are involved, this problem describes a natural transformation from functor F:A--> B to parallel functor G:A-->B to be a function t which satisfies the left and right transformation laws t(ab)=G(a)t(b)=t(a)F(b) when ab is defined in A. (The pair (G,F) is implicitly part of the natural transformation.) If A is a group with object u and G and F are group actions, then the value t(u) is a classical intertwining function, whereas I have been calling t an intertwining function. I apologize to all of those who had any of their time wasted in wondering about this connection. I still need terminology for t much more than I need the intertwining function idea; so, from now on, I intend to use "entwining function" to refer to t, but, if this conflicts with more standard usage or if there is already a standard word for t, I would appreciate being told. Pat Donaly