From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: "Vasili I. Galchin" <vigalchin@gmail.com>
Cc: Categories mailing list <categories@mta.ca>
Subject: Re: Grothendieck topology vs Lawvere-Tierney topology
Date: Fri, 9 Sep 2011 12:11:31 +0100 (BST) [thread overview]
Message-ID: <E1R236w-0007yq-7a@mlist.mta.ca> (raw)
In-Reply-To: <E1R1q39-0005H1-R6@mlist.mta.ca>
On Wed, 7 Sep 2011, Vasili I. Galchin wrote:
> In which paper did Lawvere and Tierney lay out the relationship
> between these two topologies?
>
I don't know where the proof of the equivalence was first written
down. But it was stated clearly by Lawvere in his Introduction to
Springer LNM 274 (1972):
"At the Rome and Overwolfach [sic] meetings I had pointed out that
the usual notion of a Grothendieck topology is equivalent to a
single such morphism j [that is, a Lawvere-Tierney topology];
Tierney showed that the appropriate axioms on j are simply that
jj = j and j preserves finite conjunctions."
Peter Johnstone
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-09-09 11:11 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-09-08 2:45 Vasili I. Galchin
2011-09-09 11:11 ` Prof. Peter Johnstone [this message]
2011-09-09 17:14 Fred E.J. Linton
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