Leverage UHCont and WMeas_uc to advance Conformal Prediction

Investigate how the categorical structures UHCont (objects: topological spaces; morphisms: upper hemicontinuous correspondences) and WMeas_uc (objects: measurable Polish spaces; morphisms: weakly measurable uniformly compact-valued correspondences) can be leveraged to derive additional theoretical properties, constructions, or algorithms for Conformal Prediction beyond those established in this work.

Background

The paper introduces two new categories, UHCont and WMeas_uc, and proves that the Full Conformal Prediction correspondence is a morphism in both, embedded in commuting diagrams. This categorical framing underpins intrinsic uncertainty quantification and connections across Bayesian, frequentist, and imprecise-probabilistic reasoning.

The authors suggest that these functional-analysis-flavored categorical structures may yield further insights into Conformal Prediction but do not specify concrete methods, leaving this as an explicit open question.