In this brief exposition we prove De Rham theorem, which states that De Rham and singular cohomology, over a paracompact manifold, are isomorphic. Moreover we prove the explicit form of this isomorphism, given by the integration of forms on singular simplices. This result is proved using F-injective resolutions and tools from sheaf theory.
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A short seminar I gave in Padova, in January 2020, dealing with the proof of De Rham theorem for singular and De Rham cohomology.
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