??double negation topos of presheaf topos on exponent N vs N^op ...

??in both cases you get the terminal topos, but in N case the model is an "ideal model" corresponding to +infinity, vs in N^op case it's "genuine model" corresponding to 0 ... ??or something ???...

??that is... ??"taking colimit" in N case, vs "evaluation at 0" in N^op case ...