Beschreibung:
For a quantale I, which is a unit interval endowed with a continuous triangular norm and the Barr extension β¯I of the ultrafilter monad to I-Rel, a characterization of the discrete presheaf monad associated to β¯I is given. It is also proved that, when & is the Łucasiewicz triangular norm, the discrete presheaf monad is isomorphic to the saturated prefilter monad, and when & is the product triangular norm, the prime functional ideal monad is isomorphic to a submonad of the discrete presheaf monad.