When the fiber to be integrated over is the U(1) fiber of electromagnetism, the dual pairing is such that the direction (orientation) on the fiber is reversed. When the fiber to be integrated over is the SU(3) fiber of the color charge, the dual pairing again reverses orientation. This "just works" for SU(3) because it has two dual fundamental representations formula_18 and formula_19 which can be naturally paired. This prescription for a quantum field naturally generalizes to any situation where one can enumerate the continuous symmetries of the system, and define duals in a coherent, consistent fashion. The pairing ties together opposite charges in the fully abstract sense. In physics, a charge is associated with a generator of a continuous symmetry. Different charges are associated with different eigenspaces of the Casimir invariants of the universal enveloping algebra for those symmetries. This is the case for "both" the Lorentz symmetry of the underlying spacetime manifold, "as well as" the symmetries of any fibers in the fiber bundle posed above the spacetime manifold. Duality replaces the generator of the symmetry with minus the generator. Charge conjugation is thus associated with reflection along the line bundle or determinant bundle of the space of symmetries.