Predicate Transformers, (co)Monads and Resolutions

Pierre Hyvernat (1, 2)

1 LAMA - Laboratoire de Mathématiques
2 IML - Institut de mathématiques de Luminy

This short note contains random thoughts about a factorization theorem for closure/interior operators on a powerset which is reminiscent to the notion of resolution for a monad/comonad. The question originated from formal topology but is interesting in itself. The result holds constructively (even if it classically has several variations); but usually not predicatively (in the sense that the interpolant will no be given by a set). For those not familiar with predicativity issues, we look at a ``classical'' version where we bound the size of the interpolant.

Domaines: Logique en informatique [cs.LO]

Pierre Hyvernat. Predicate Transformers, (co)Monads and Resolutions. 2004. ⟨hal-00395633⟩