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The purpose of this note is to define sheaves for diffeological spaces andgive a construction of their \v{C}ech cohomology. As an application, we provethat the first degree \v{C}ech cohomology classes for the sheaf of smoothfunctions to an abelian diffeological group $G$ classify the diffeologicalprincipal $G$-bundles.

Sheaves, principal bundles, and \v{C}ech cohomology for diffeological spaces