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 !