 We already know, from the relation of the BRST operator to the exterior derivative and the Faddeev–Popov ghost to the Maurer–Cartan form, that the ghost "c" corresponds (up to a phase) to a formula_8-valued 1-form on formula_50.In order for integration of a term like formula_59 to be meaningful, the anti-ghost formula_55 must carry representations of these two Lie algebras—the vertical ideal formula_50 and the gauge algebra formula_8—dual to those carried by the ghost.In geometric terms, formula_55 must be fiberwise dual to formula_8 and one rank short of being a top form on formula_50.