* Re: Grothendieck topology vs Lawvere-Tierney topology
@ 2011-09-09 17:14 Fred E.J. Linton
0 siblings, 0 replies; 3+ messages in thread
From: Fred E.J. Linton @ 2011-09-09 17:14 UTC (permalink / raw)
To: categories
On Fri, 09 Sep 2011 11:40:07 AM EDT Peter Johnstone
<P.T.Johnstone@dpmms.cam.ac.uk> wrote:
> 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) ...
And that was recording the upshot of work carried out in the course of
a 1969-70 seminar on topos theory held at Dalhousie U. (Halifax, NS),
during a sort of follow-on to the marvelous Zurich Triples Book year
at the ETH during 1966-67.
Thanks for that Dalhousie year, btw, to Bill Lawvere, Arnold J. Tingley,
and the Izaak Walton Killam Foundation, without whose organizational
efforts, cooperation, and funding, respectively, there'd have been
no critical mass for that year at all.
Cheers, -- Fred
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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* Re: Grothendieck topology vs Lawvere-Tierney topology
2011-09-08 2:45 Vasili I. Galchin
@ 2011-09-09 11:11 ` Prof. Peter Johnstone
0 siblings, 0 replies; 3+ messages in thread
From: Prof. Peter Johnstone @ 2011-09-09 11:11 UTC (permalink / raw)
To: Vasili I. Galchin; +Cc: Categories mailing list
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/ ]
^ permalink raw reply [flat|nested] 3+ messages in thread
* Grothendieck topology vs Lawvere-Tierney topology
@ 2011-09-08 2:45 Vasili I. Galchin
2011-09-09 11:11 ` Prof. Peter Johnstone
0 siblings, 1 reply; 3+ messages in thread
From: Vasili I. Galchin @ 2011-09-08 2:45 UTC (permalink / raw)
To: Categories mailing list
Hello,
In which paper did Lawvere and Tierney lay out the relationship
between these two topologies?
Regards,
Vasili
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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