  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.
  More strikingly, Markov categories give a notion of determinism for sources
and channels, and we can define entropy exactly by measuring how far a source
or channel is from being deterministic. This recovers Shannon and R\'enyi
entropies, as well as the Gini-Simpson index used in ecology to quantify
diversity, and it can be used to give a conceptual definition of generalized
entropy.
