From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2358 Path: news.gmane.org!not-for-mail From: Philip Wadler Newsgroups: gmane.science.mathematics.categories Subject: "twisted" Galois connections? Date: Tue, 17 Jun 2003 12:25:23 -0400 Message-ID: <200306171625.h5HGPNg07087@kira.research.avayalabs.com> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018601 3745 80.91.229.2 (29 Apr 2009 15:23:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:23:21 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jun 17 16:33:19 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Jun 2003 16:33:19 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19SM8G-0004ms-00 for categories-list@mta.ca; Tue, 17 Jun 2003 16:28:40 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 49 Original-Lines: 40 Xref: news.gmane.org gmane.science.mathematics.categories:2358 Archived-At: Is anything known about the following variation on a Galois connection? Given domains X and A with partial orders, f:X->A and g:A->X constitute a *Galois connection* if the following four conditions hold (1) x <= y implies f(x) <= f(y) (2) a <= b implies g(a) <= g(b) (3) x <= g(f(x)) (4) f(g(a)) <= a (This is equivalent to saying f(x) <= a iff x <= g(a).) The same functions constitute a *twisted Galois connection* if we have conditions (1)-(3) and also (4') a <= f(g(a)) Both Galois connections and twisted Galois connections compose. If f:X->A, g:A->X and h:A->Z, k:Z->A consitute a (twisted) Galois connection, then so do f;h:X->Z, k;g:Z->X. Is there anything in the literature about twisted Galois connections or the corresponding notion of a twisted adjoint, perhaps under a different name? Many thanks, -- P ----------------------------------------------------------------------- Philip Wadler wadler@avaya.com www.research.avayalabs.com/user/wadler Avaya Labs, 233 Mount Airy Road, Basking Ridge, NJ 07920 USA phone +1 908 696 5137 fax +1 908 696 5402 ---------------------------------------------------------------------- "When a Mathematical Reasoning can be had it's as great a folly to make use of any other, as to grope for a thing in the dark, when you have a Candle standing by you." John Arbuthnot, 1692 ----------------------------------------------------------------------