Chapter 77: The Categorical Imperative as Sheaf Condition

Kant’s categorical imperative is extracted as a naturality constraint on the presheaf of admissible enactments. Universalizability — “act only on that maxim which you can will as universal law” — becomes the requirement that local enactments glue into a global section over the site of all rational perspectives. The CI as Naturality Constraint (VII.D66) formalizes the imperative as a natural transformation, and the CI-Sheaf Equivalence (VII.T31) proves that a maxim is universalizable if and only if it satisfies the sheaf condition on the dignity-filtered site. Failure modes are classified: dignity breaks, Čech obstructions (contradiction in conception), and tension obstructions (contradiction in will).