[note from moderator: apologies to Colin for delayed posting...Bob] "Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk> wrote of $\Omega$ as subobject classifier:
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.
I have heard that too. And I am sure it is not in the published SGA4. I have one mimeographed version in my office. Omega does not occur there the sections on topologies, but next week I will look to see if it occurs as an example of a sheaf--unless someone who knows writes in sooner. best, Colin _________________________________________ Dialectic, the purest part of philosophy, hovers attentively over mathematics, encompasses its whole development, and of itself contributes to the special sciences their various perfecting, critical, and intellective powers--the powers, I mean, of analysis, division, definition, and demonstration. --Proclus, ca. 460 AD, A COMMENTARY ON THE FIRST BOOK OF EUCLID'S ELEMENTS