This paper presents a category-theoretic approach to address the conceptual ambiguity surrounding Conformal Prediction (CP). While CP is an uncertainty representation technique that provides a finite sample-corrected prediction space, we highlight its limitations in quantitatively quantifying uncertainty. By structuring CP into two newly defined categories, we demonstrate that CP is essentially an uncertainty quantification (UQ) mechanism, providing a bridge between Bayesian, frequentist, and uncertainty-based approaches. Furthermore, by demonstrating that CPR is an image of a covariant function, we demonstrate that locally added privacy noise does not violate global applicability guarantees.
