Sheaves, principal bundles, and Čech cohomology for diffeological spaces

Derek Krepski, Jordan Watts, Seth Wolbert

Published 2021-11-01, updated 2022-09-26Version 2

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.