Dear all, Any functor from a small category A to a complete category E induces a contravariant adjunction between E and Set^A. This in turn induces a monad on E, the "codensity monad" of the functor. (The construction of the adjunction is better known in its dual form, starting with a functor from a small category to a COcomplete category. For example, the usual functor from Delta into Top induces the usual adjunction between topological spaces and simplicial sets.) The codensity monad of the inclusion FinSet --> Set is the ultrafilter monad. This seems a rather basic fact, but I've been unable to find it in the literature. I'd be grateful if someone could tell me a reference. (I'm aware of the 1987 paper by Reinhard Börger giving a different but related characterization of the ultrafilter monad.) Thanks, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]