Differential forms on $C^\infty$-ringed spaces

We construct a complex of differential forms on a local $C^\infty$-ringed space. The two main classes of spaces we have in mind are differential spaces in the sense of Sikorski and $C^\infty$-schemes. Just as in the case of manifolds the construction is functorial. Consequently forms can be integrated over simplices and Stokes' theorem holds.

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