From: Galchin Vasili <vngalchin@yahoo.com>
To: categories@mta.ca
Subject: More Topos questions ala "Conceptual Mathematics"
Date: Wed, 19 Feb 2003 16:16:51 -0800 (PST) [thread overview]
Message-ID: <20030220001651.79067.qmail@web12201.mail.yahoo.com> (raw)
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 <alpha, beta> 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
next reply other threads:[~2003-02-20 0:16 UTC|newest]
Thread overview: 12+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-02-20 0:16 Galchin Vasili [this message]
2003-02-20 18:48 ` Stephen Schanuel
2003-02-21 0:57 ` Vaughan Pratt
2003-06-10 21:23 ` Galchin Vasili
[not found] <schanuel@adelphia.net>
2004-03-04 5:44 ` mystification and categorification Stephen Schanuel
2004-03-05 16:55 ` David Yetter
2004-03-06 6:49 ` Vaughan Pratt
2004-03-07 21:04 ` Mike Oliver
2004-03-08 10:20 ` Steve Vickers
2004-03-07 19:43 ` Tom Leinster
2004-03-09 10:54 ` Pawel Sobocinski
2004-03-12 13:50 ` Quillen model structure of category of toposes/locales? Vidhyanath Rao
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