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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. Under mild conditions, we prove a commuting diagram result that decomposes the construction of a conformal region into two steps: Extracting a set of predictive distributions from the data, and then deriving a prediction region from this set. This decomposition provides a principled route to numerical uncertainty summaries beyond region size. We further prove an asymptotic compatibility result showing that, for Bayesian predictive scores in regular regimes, conformal regions converge","title":"A Category-Theoretic Analysis of Conformal Prediction","url":"https://arxiv.org/abs/2507.04441","vendor":"arxiv_cs_ai"},"summary":"arXiv:2507.04441v4 Announce Type: replace-cross \nAbstract: 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. Under mild conditions, we prove a commuting diagram result that decomposes the construction of a conformal region into two steps: Extracting a set of predictive distributions from the data, and then deriving a prediction region from this set. This decomposition provides a principled route to numerical uncertainty summaries beyond region size. 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