Request for a reference

Request for a reference

[Garraway, Dale]

Hi All

Could some one please send me a reference of the fact that the category of
presheaves on a Heyting algebra $H$ is equivalent to the category of
sheaves on the Heyting algebra of down closed subsets of $H$.  I believe
this is true in general for any partial order so a reference to either
would be greatly appreciated.

Dale Garraway
Dept. of Math, 
Eastern Washington
dgarraway@ewu.edu



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Re: Request for a reference

[Paul B Levy]

Dear Dale,

I don't know if it appeared anywhere earlier, but the result for an
arbitrary poset is Proposition 8.4 in Birkedal, Mogelberg, Schwinghammer
and Stovring's paper "First steps in synthetic domain theory:
step-indexing in the topos of trees".

http://www.cs.au.dk/~birke/papers/sgdt-journal.pdf

Paul



On 12/11/14 18:46, Garraway, Dale wrote:
>
> Hi All
>
> Could some one please send me a reference of the fact that the category of
> presheaves on a Heyting algebra $H$ is equivalent to the category of
> sheaves on the Heyting algebra of down closed subsets of $H$.  I believe
> this is true in general for any partial order so a reference to either
> would be greatly appreciated.
>
> Dale Garraway
> Dept. of Math,
> Eastern Washington
> dgarraway@ewu.edu

-- 
Paul Blain Levy
School of Computer Science, University of Birmingham
http://www.cs.bham.ac.uk/~pbl


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