We categorify the adjunction between locales and topological spaces, this amounts to an adjunction between (generalized) bounded ionads and topoi. We show that the adjunction is idempotent, yielding a biequivalence between topoi with enough points and sober bounded ionads. We relate this adjunction to the Scott adjunction, which was discussed from a more categorical point of view in previous work. We hint at the logical implications of this result in terms of completeness/reconstruction theorems.
De Dustin Clausen
De Riccardo Zanfa
De Jean-Claude Belfiore
De Daniel Bennequin
De Samson Abramsky
De Jens Hemelaer
De Francesco Genovese
De Clément Delcamp
De Clément Delcamp
