Category-Theoretical Evaluation of Abstraction between Causal Models
Causal models offer a rigorous formalism to express causal relations between variables of interest. Causal systems may be represented at different levels of granularity or abstraction; think, for example, to microscopic and macroscopic descriptions of thermodynamics systems. Reasoning about the relationship between causal models at different levels of abstraction is a non trivial problem.
In this notebook we provide a tutorial introduction to the categorical framework proposed by Rischel which relies on a category theory formalization to evaluate and measure the approximation (or error) introduced by abstractions between causal models. We illustrate ideas and concepts running simulations inspired by the examples provided by the author, and we then discuss the meaning and the implications of the results.