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/ ]
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/ ]
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/ ]
participants (3)
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Fred E.J. Linton -
Prof. Peter Johnstone -
Vasili I. Galchin