Deriving the Standard Model Gauge Group from a Single Category-Theoretic Axiom

The Standard Model gauge group U(1) × SU(2) × SU(3) is empirically established but not derived from first principles. We show that the complete gauge group structure, including the direct product topology and the termination of the gauge hierarchy, follows from a single category-theoretic postulate: a self-dual simple object A ≅ A* in a ℂ-enriched semiadditive dagger-compact category C₀, whose compact closure provides pair creation and annihilation morphisms. Specifically, U(1) arises as the automorphism group of the simple object A via Schur's lemma, SU(2) as the traceless dagger-automorphisms of A ⊕ A via the Lie decomposition u(2) = u(1) ⊕ su(2), and SU(3) as the dagger-automorphisms of Sym²(ℂ²) = ℂ³ via monoidal elimination and the symmetric square. A Higgs constraint theorem demonstrates that spontaneous symmetry breaking is possible only at the first hierarchical level, so that SU(3) confines and the hierarchy halts. The derivation produces seven testable predictions, five of which exclude classes of beyond-Standard-Model physics, together with two derived consequences consistent with the framework. All predictions are consistent with current observations. Highlights: • Standard Model gauge group derived from a single category-theoretic postulate • Direct product topology proven, excluding grand unification • Higgs constraint theorem terminates the gauge hierarchy at three factors • Seven testable predictions, five excluding BSM physics classes • Dagger-compact categories applied to gauge group derivation