2023
DOI: 10.48550/arxiv.2303.03251
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Diffeological Čech cohomology

Abstract: Motivated by problems in which data are given over covering generating families, we suggest a new cohomology theory for diffeological spaces, called diffeological Čech cohomology, which is an exact ∂ -functor of the section functor for sheaves on diffeological spaces. As applications, under the situations of a setup, i) the generalized Mayer-Vietoris sequence for a diffeological space is established; ii) a version of the de Rham theorem is obtained, which connects diffeological Čech cohomology to the de Rham c… Show more

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