Free gs-monoidal categories and free Markov categories

Understand

Categorical probability has recently seen significant advances through the formalism of Markov categories, within which several classical theorems have been proven in entirely abstract categorical terms.

• Closely related to Markov categories are gs-monoidal categories, also known as CD categories.
• These omit a condition that implements the normalization of probability.
• Extending work of Corradini and Gadducci, we construct free gs-monoidal and free Markov categories generated by a collection of morphisms of arbitrary arity and coarity.