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A C-infinity ring is a set equipped with n-ary operations corresponding tosmooth n-ary functions on the real line (satisfying natural axioms). We provethat the cosimplicial abelian group associated to the de Rham complex ofEuclidean space has the structure of a cosimplicial C-infinity ring. We alsoanalyse the notion of R-module (following Quillen) for a (co-)simplicialC-infinity ring R.

Cosimplicial C-infinity rings and the de Rham complex of Euclidean space