From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2191 Path: news.gmane.org!not-for-mail From: Galchin Vasili Newsgroups: gmane.science.mathematics.categories Subject: More Topos questions ala "Conceptual Mathematics" Date: Wed, 19 Feb 2003 16:16:51 -0800 (PST) Message-ID: <20030220001651.79067.qmail@web12201.mail.yahoo.com> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 X-Trace: ger.gmane.org 1241018478 2941 80.91.229.2 (29 Apr 2009 15:21:18 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:21:18 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Feb 20 12:27:23 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 20 Feb 2003 12:27:23 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18ltWe-0006rB-00 for categories-list@mta.ca; Thu, 20 Feb 2003 12:26:20 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 47 Original-Lines: 17 Xref: news.gmane.org gmane.science.mathematics.categories:2191 Archived-At: Hello, 1) In the very last chapter (Session 33 "2: Toposes and logic" of "Conceptual Mathematics" where the authors cover topoi, they define '=>' for the internal Heyting algebra of Omega: "Another logical operation is 'implication', which is denoted '=>'. This is also a map Omega x Omega->Omega, defined as the classifying map of the subobject S 'hook' Omega x Omega determined by the all those in Omega x Omega such that alpha "subset of" beta." Starting from "subobject S 'hook" ......" I got totally lost. I am frustrated because I know this is crucial to understanding why Omega is an internal Heyting algebra, so any help would be appreciated. (I am assuming that alpha and beta are subojects of Omega???). 2) In the same Session 33 on pg 350 is a set "rules of logic". These are exactly the axioms for a Heyting algebra, yes? Regards, Bill Halchin