  For a number of locally finitely presentable categories K we describe the
codensity monad of the full embedding of all finitely presentable objects into
K. We introduce the concept of D-ultrafilter on an object, where D is a "nice"
cogenerator of K. We prove that the codensity monad assigns to every object an
object representing all D-ultrafilters on it. Our result covers e.g. categories
of sets, vector spaces, posets, semilattices, graphs and M-sets for finite
commutative monoids M.
