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From: "Prof. Peter Johnstone"
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Subject: Re: Grothendieck topology vs Lawvere-Tierney topology
Date: Fri, 9 Sep 2011 12:11:31 +0100 (BST)
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To: "Vasili I. Galchin"
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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
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