Type-Theoretic Perspectivalism, Sheaf-Theoretic Synthetic Universality, and Transcendental AI Governance

Contemporary advances in homotopy type theory and sheaf theory make possible a synthetic transcendentalism that reconciles Husserlian phenomenology with Badiouian ontology—and in doing so, provides a non-moral, non-mythic foundation for AI governance. Gabriel Catren's type-theoretic perspectivalism and Fernando Zalamea's sheaf-theoretic synthetic universality converge in what I have termed "transcendental mathematics'': a compatibilist framework wherein mathematical structures emerge through the interaction of constitutive activity and objective constraints, making them at once perspectival and real. This approach stands opposed to the dominant alternatives. Anna Greenspan's Deleuzean transcendental materialism, with its planes of Chronos and Aeon, dissolves concrete mechanism into poetic abstraction. Nick Land's cybernetic reading of Kant collapses difference into a dogmatic apparatus of control. And the Jungian archetypal worldview, as Padusniak has shown, substitutes counterfeit religiosity for genuine insight. Against all these, I contend that the categorical and type-theoretic structures of mathematics impose a priori constraints on thought and action that are neither arbitrary moral impositions nor mythic projections. These structural constraints, already operative in the planetary techno-social stack, should form the basis of AI governance. The transcendental of AI is not an archetype or a code, but a type, a category, a sheaf.