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extending ∇. The covariant exterior derivative is characterized by [[linearity]] and the equation
:<math>d_\nabla(\omega\wedge\eta) = d_\nabla\omega\wedge\eta + (-1)^p\,\omega\wedge d\eta</math>
where ω is a ''E''-valued ''p''-form and η is an ordinary ''q''-form. In general, one need not have ''d''<sub>∇</sub><sup>2</sup> = 0. In fact, this happens if and only if the connection ∇ is flat (i.e. has vanishing [[curvature form|curvature]]).
==Lie algebra-valued forms==
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