Post #2278881

@julesh@mathstodon.xyz @lisyarus@mastodon.gamedev.place This is a baby version of Stone duality, ie the fact that Set^op is equivalent to the category of complete atomic boolean algebras : in one direction, you map a set to its powerset, which is a CABA ; in the other direction, you map a CABA to its set of atoms (elements x st y < x implies y = ⊥). Indeed, the atoms in a powerset are exactly the singletons, and a set is isomorphic to the set of its singleton. (The good thing is that this is nicely structural, and does not need to play set-theoretic trickery with unions or some such.)