Causal Abstractions, Categorically Unified

We introduce a categorical framework for causal abstraction that unifies and extends existing approaches. Modeling causal systems as Markov functors from free Markov categories generated by directed acyclic graphs, we define a causal abstraction as a deterministic natural transformation together with an embedding of restricted free Markov categories. This separates graphical compatibility under interventions from domain-level clustering of variables or values. Our framework provides an explicit characterization of admissible high-level graphs and recovers prior notions such as constructive -abstractions and cluster-DAG abstractions with unobserved confounders. We give concise categorical proofs that interventional distributions factorize over graphical abstractions and that do-calculus applied to the high-level graph yields valid conclusions for the low-level model.