  We extend to a scheme-theoretic context the notion of a combinatorial
differential form, due to A.Kock in the framework of synthetic differential
geometry. We show that group-valued combinatorial forms on a scheme may be
identified, under very general hypotheses, with traditional Lie algebra-valued
differential forms, and that their Lie algebra structure can be recovered from
first principles. Some basic results from differential geometry (Maurer-Cartan
equation, Bianchi identity), as well as a higher analogue, are obtained by
exploiting this identification.
