Markov Categories and Entropy

Understand

Markov categories are a novel framework to describe and treat problems in probability and information theory.

• In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities.
• We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric.
• As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components.