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.
By Dustin Clausen
By Riccardo Zanfa
By Jean-Claude Belfiore
By Daniel Bennequin
By Samson Abramsky
By Jens Hemelaer
By Francesco Genovese
By Clément Delcamp
By Christoph Koutschan
By Christoph Koutschan
By Christiane Koch
By Misha Gromov
By Céline Duval
By Olivier Benoist
