On saturated prefilter monads

Abstract

In this paper we show that the prime saturated prefilter monads are sup-dense and interpolating in saturated prefilter monads. It follows that CNS spaces are the lax algebras for prime saturated prefilter monads. As for the algebraic part, we prove that the Eilenberg-Moore algebras for saturated prefilter monads are exactly continuous I-lattices.

Keywords

• eilenberg-moore algebra
• prime saturated prefilter monad
• saturated prefilter monad