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Hello !

If I'm not mistaken, an atomic topos decompose as a disjoint sum of connected atomic topos, and Connected Atomic topos with a point corresponds to classifying topos of localic groups.

But what about conected atomic topos without point ? do we know what they look like ?

I actually know no example of these non-spatial atomic topos. So if a 'classification' of them is not possible, any example will already be interesting.

Thank you !

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There is an example of a pointless connected atomic topos: see Example 3.4.14 in [Sketches of an elephant, Part D]. –  Zhen Lin Jun 18 '13 at 22:13
    
I added the [ct.category-theory] tag. –  David Roberts Jun 18 '13 at 22:33
    
@Zhen - why not add that as an answer, or even better, write it out? Not everyone has access to the Elephant (it does cost a small fortune after all). –  David Roberts Jun 18 '13 at 22:34
    
I would if I understood the construction myself! –  Zhen Lin Jun 18 '13 at 22:52
    
@David, concerning Elephants, contact me. I don't seem to have your current email address. –  Urs Schreiber Jun 18 '13 at 23:15

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