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created focal point
Interesting – I was expecting to see something about optics from a mathematical physics perspective. :-) Does anyone else besides Freyd-Scedrov use this terminology? (Although it doesn’t seem so bad – it’s almost opposite to “generic point”, i.e., a maximally smeared-out point.)
Added a few examples to focal point.
Right. This was a link long time ago demanded by local topos. I simply wanted to un-gray that link. Eventually we should add a diambiguation and some physics there!
Incidentally, is the Freyd cover of a Grothendieck topos $E$ a local topos over $Set$? It sort of feels like it wants to be, if we intuitively think of the Freyd cover as the result of adjoining a generic focal point to the “space” $E$, as it were.
Isn’t this what Mike pointed out? Attributing it to C3.6.5 of the Elephant.
Okay, thanks Urs. I haven’t been following a lot of these discussions at all closely, because I’ve largely been away from mathematics period. (And, you and Mike have been covering a lot of ground recently.)
I have added a brief remark to this extent here. Maybe the more precise reference to Johnstone is: lemma C3.6.4.
You have a great intuition, Todd! I don’t know that I would have come up with that immediately after seeing the definition of focal point.
Thanks, Urs!
Added to focal point the example of the prime spectrum of a local ring and the locale theoretical characterisation.
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