categories: Re: the alpha of Omega

[John Duskin <duskin@math.buffalo.edu>]

[note from moderator: apologies to Jack for the delayed posting...Bob]

>On Mon, 27 Aug 2001, Keith Harbaugh wrote:
>
>>  While the topic of topos subobject classifier is current,
>>  how far back can the historical and conceptual origins
>>  of the use of "$\Omega$" as the symbol denoting such be traced?
>>
>>  Regards,
>>  Keith Harbaugh
>>
>I seem to recall being told that it occurs somewhere in the
>original (mimeographed) version of SGA4 (as an interesting
>example of a sheaf on a site), and that Lawvere and Tierney
>borrowed the notation that Grothendieck et al. had used for it.
>However, I've never been able to find it there myself; I'm
>pretty sure it's not in the revised version published in
>Springer Lecture Notes.
>
>Peter Johnstone


-- 
I just got out my old original mimeographed copy of SGA 4 Fasicule 1 
(by Verdier) and I'm afraid that I can't find it there either. Quite 
consistently, $\Omege$ is used there only to denote a generic 
topological space: " Soient $\Omega$ un espace topologique, 
$\Omega^{\tilde}$ le topos des faisceaux d'ensembles sur 
$\Omega$...." etc.

Also I seem to recall hearing that when Grothendieck saw the 
Lawvere-Tierney subobject classifier $\Omega$ he was amazed that they 
could have missed the centrality of such a powerful notion in Topos 
Theory. He always subsequently referred to it  technically as "the 
Lawvere element"!

But to settle this, at least partly, why don't we just ask Bill or 
Myles to tell us where they got the $\Omega$ notation?

Jack Duskin