Infinitesimal Causality

The paper presents a categorical framework for infinitesimal causality within Frobenius Markov categories, utilizing tangent-bundle semantics to model interventions as tangent deformations in information structures. It defines categorical causal sufficiency and explores the interaction between categorical and geometric Frobenius structures, highlighting the role of interventions as tangent vectors that influence classical information flow. This work is significant for practitioners as it provides a formalism that enhances understanding of causal inference and intervention modeling, which could improve the design of algorithms in structural causal models.