Lemma 6.22.1. Let $f : X \to Y$ be a continuous map.

Let $\mathcal{G}$ be an abelian presheaf on $Y$. Let $x \in X$. The bijection $\mathcal{G}_{f(x)} \to (f_ p\mathcal{G})_ x$ of Lemma 6.21.4 is an isomorphism of abelian groups.

Let $\mathcal{G}$ be an abelian sheaf on $Y$. Let $x \in X$. The bijection $\mathcal{G}_{f(x)} \to (f^{-1}\mathcal{G})_ x$ of Lemma 6.21.5 is an isomorphism of abelian groups.

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