Suppose $\mathcal F_n$ is an inverse system of sheaves over a topological space $X$, and let $\mathcal F$ be their inverse limit. Then for any $x\in X$, do we have $\mathcal F_x=\varprojlim \mathcal F_{n,x}$? I think it is not true.. But could you provide a counterexample(or just prove it)?
2026-04-08 23:04:56.1775689496
Does inverse limit commute with stalk?
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