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Sheaves, principal bundles, and Čech cohomology for diffeological spaces
Published 1 Nov 2021 in math.DG and math.AT | (2111.01032v2)
Abstract: The purpose of this note is to define sheaves for diffeological spaces and give a construction of their \v{C}ech cohomology. As an application, we prove that the first degree \v{C}ech cohomology classes for the sheaf of smooth functions to an abelian diffeological group $G$ classify the diffeological principal $G$-bundles.
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