On Discrete Presheaf Monads - Gao Zhang; Shaoqun Zhang (Axioms, 2023)
For a quantale <semantics>I</semantics>, which is a unit interval endowed with a continuous triangular norm and the Barr extension <semantics><mover>β¯</mover>I</semantics> of the ultrafilter monad to <semantics>I-Rel,</semantics> a characterization of the discrete presheaf monad associated to <semantics><mover>β¯</mover>I</semantics> 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.