A Category-Theoretic Analysis of Conformal Prediction

ArXi:2507.04441v4 Announce Type: replace-cross Conformal prediction (CP) produces prediction regions with finite-sample, distribution free coverage guarantees, but its interpretation as a quantitative uncertainty tool is often left implicit. We develop a category-theoretic approach that makes this structure explicit. We show that Full Conformal Prediction can be represented as a morphism in two categories capturing (i) stability of set-valued procedures and (ii) measurability of random regions.