Bimonoidal Structure of Probability Monads

Understand

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability.

• This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e.
• a bimonoidal structure).
• If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength.