Is there a deRham (co)homology for vector-valued differential forms?
The deRham (co)homology of differential forms has been well-discussed and well-founded, along with the fact that for the exterior derivative on differential forms, $d$, with $d^2 =0$, then there's a deRham (co)homology.
What about the covariant exterior differential $D$ on vector-valued differential form? Can a (co)homology be defined?