<p>We offer a category-theoretic representation of the process theory of causality. The new formalism allows process theorists to (i) explicate their explanatory strategies (etiological and constitutive explanations) using the compositional features of string diagrams; (ii) probabilistically evaluate causal effects through the categorical notion of functor; (iii) address the problem of explanatory irrelevance via diagram surgery; and (iv) provide a theoretical explanation for the difference between conjunctive and interactive forks. We also claim that the fundamental building blocks of the process theory—namely processes, interactions, and events—can be modeled using three types of morphisms. Overall, categorical modeling demonstrates that the philosophical theory of process causality possesses scientific rigor and expressive power comparable to those of its event-based counterparts, such as causal Bayes nets.</p>