Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 18 1 2023 02 01 On saturated prefilter monads 19 41 102934 10.52547/cgasa.2022.102934 EN Gao Zhang Institute of Mathematics, Nanjing Normal University, Nanjing, China Wei He Institute of Mathematics, Nanjing Normal University Journal Article 2022 12 13 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. https://cgasa.sbu.ac.ir/article_102934_898a0e46882c081b09170b0fe72108f4.pdf