[Haskell-cafe] "Prime" monads?

Haskellians, Is there a characterization of "prime" monads? Here the notion of factorization i'm thinking about is decomposition into adjoint situations. For example, are there monads for which there are only the Kleisli and Eilenberg-Moore decompositions into adjoint situations? Would this be a characterization of quintessentially "free" or "generative"? Best wishes, --greg -- L.G. Meredith Managing Partner Biosimilarity LLC 505 N 72nd St Seattle, WA 98103 +1 206.650.3740 http://biosimilarity.blogspot.com