Kleisli enriched
نویسنده
چکیده
For a monad S on a categoryK whose Kleisli category is a quantaloid, we introduce the notion of modularity, in such a way that morphisms in the Kleisli category may be regarded as V(bi)modules (= profunctors, distributors), for some quantale V . The assignment S // V is shown to belong to a global adjunction which, in the opposite direction, associates with every (commutative, unital) quantale V the prototypical example of a modular monad, namely the presheaf monad on VCat, the category of (small) V-categories. We discuss in particular the question whether the Hausdorff monad on VCat is modular.
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