Definition 6.21.7. Let $f : X \to Y$ be a continuous map. Let $\mathcal{F}$ be a sheaf of sets on $X$ and let $\mathcal{G}$ be a sheaf of sets on $Y$. An *$f$-map $\xi : \mathcal{G} \to \mathcal{F}$* is a collection of maps $\xi _ V : \mathcal{G}(V) \to \mathcal{F}(f^{-1}(V))$ indexed by open subsets $V \subset Y$ such that

commutes for all $V' \subset V \subset Y$ open.

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