Internal Kleisli categories

Recursive Types in Kleisli Categories

We show that an enriched version of Freyd's principle of versality holds in the Kleisli category of a commutative strong monad with xed-point object. This gives a general categorical setting in which it is possible to model recursive types involving the usual datatype constructors.

Intermodeling, Queries, and Kleisli Categories

Specification and maintenance of relationships between models are vital for MDE. We show that a wide class of such relationships can be specified in a compact and precise manner if intermodel mappings involve derived model elements computed by corresponding queries. Composition of such mappings is not straightforward and requires specialized algebraic machinery. We present a formal framework, i...

From Kleisli Categories to Commutative C *-Algebras: Probabilistic Gelfand Duality

C -algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to incorporate various styles of computation (set-theoretic, probabilistic, quantum) inside categories of C -algebras. At first, this paper concentrates on the com...

Kleisli enriched

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 ...

Internal Categories and Quantum Groups