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EDIT: Let $\mathcal{F},\mathcal{G}$ be sheaves of abelian groups on a topological space $X$. Then there exists a canonical cup product $$H^i(X,\mathcal{F})\otimes_\mathbb{Z}H^j(X,\mathcal{G})\to H^{i+...

I have been trying to understand the proof of the following theorem for the last month, I read some basics of sheaves theory and their cohomology, but still can't get the idea of this important ...