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Stalks and points Recall that a point of a topos \(\mathcal{E}\) is a geometric morphism from the topos \(Set\). My preferred way to think about this is to consider the sheaf topos \(Sh(X)\) on some (sober) topological space \(X\). Then given \(x \in X\) and a sheaf \(S\), we can form the stalk at \(x\) \(S_x := \operatorname{colim}_{x \in U \subseteq X \text{ open}} S(U)\) This determines the…
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