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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated [[focal point]]

   created focal point

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexInteresting -- 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]].

   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.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexRight. 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!

   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!

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexIncidentally, 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.

   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.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexIsn't this what Mike [pointed out](http://golem.ph.utexas.edu/category/2011/11/discreteness_concreteness_fibr.html#more)? Attributing it to C3.6.5 of the Elephant.

   Isn’t this what Mike pointed out? Attributing it to C3.6.5 of the Elephant.

6. • CommentRowNumber6.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexOkay, 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.)

   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.)

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added a brief remark to this extent [here](http://ncatlab.org/nlab/show/Freyd%20cover#AsALocalTopos). Maybe the more precise reference to Johnstone is: lemma C3.6.4.

   I have added a brief remark to this extent here. Maybe the more precise reference to Johnstone is: lemma C3.6.4.

8. • CommentRowNumber8.
   • CommentAuthorMike Shulman
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexYou 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.

   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.

9. • CommentRowNumber9.
   • CommentAuthorTodd_Trimble
   • CommentTimeDec 7th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexThanks, Urs!

   Thanks, Urs!

10. • CommentRowNumber10.
    • CommentAuthorIngoBlechschmidt
    • CommentTimeDec 30th 2013
    • PermaLink
    Author: IngoBlechschmidt
    Format: MarkdownItexAdded to _[[focal point]]_ the example of the prime spectrum of a local ring and the locale theoretical characterisation.

    Added to focal point the example of the prime spectrum of a local ring and the locale theoretical characterisation.