Further reading

The graphical and interventionist foundations are developed in Pearl [ 2009b ] and Spirtes et al. [ 2000 ] ; the potential-outcome perspective is represented by Rubin [ 2005 ] and Imbens and Rubin [ 2015 ] . These traditions clarify why an intervention protocol must be distinguished from an arbitrary distribution shift.

For categorical probability, Fritz [ 2020 ] develops Markov categories, Cho and Jacobs [ 2017 ] treats Bayesian inversion diagrammatically, and Fritz and Klingler [ 2023 ] gives a categorical account of \(d\)-separation. String-diagram surgery [ Jacobs et al. , 2018 ] , Universal Causality [ Mahadevan , 2023 ] , and intuitionistic \(j\)-do-calculus [ Mahadevan , 2025c ] explore alternative categorical semantics for causal reasoning. Infinitesimal Causality is complementary: it studies first-order response fields and their closure, and therefore requires additional identification assumptions before a geometric obstruction becomes a causal claim.