Directed acyclic graphical (DAG) models are one of the most widely used frameworks for causal modeling. In this talk, we present a category-theoretic treatment of DAG models by associating each DAG with a free Markov category in a canonical way. This framework enables us to study key concepts in causal reasoning from an abstract perspective, including causal independence/separation, causal conditionals, and decomposition of intervention effects. Our results abstract away from the specifics of common causal models such as causal Bayesian networks, making them both more widely applicable and conceptually clearer. Notably, we show that the 'causal core' of the celebrated do-calculus can be unified in a single principle of modularity.