  Kock [Bull. Austral. Math. Soc., 25 (1982), 357-386] has considered
differential forms with values in a group in a context where neighborhood
relations are available. By doing so, he has made it clear where the so-called
Maurer-Cartan formula should come from. In this paper, while we retain the
classical definition of differential form with values in the Lie algebra of a
group, we propose another definition of coboundary operator for the de Rham
complex in a highly general microlinear context, in which neighborhood
relations are no longer in view. Using this new definition of the coboundary
operator, it is to be shown that the main result of Kock's paper mentioned
above still prevails in our general microlinear context. Our considerations
will be carried out within the framework of groupoids.
