Lemma 6.21.8. 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 $Y$. There are canonical bijections between the following three sets:
The set of maps $\mathcal{G} \to f_*\mathcal{F}$.
The set of maps $f^{-1}\mathcal{G} \to \mathcal{F}$.
The set of $f$-maps $\xi : \mathcal{G} \to \mathcal{F}$.
Comments (8)
Comment #5955 by Kevin Buzzard on
Comment #5956 by Nicolás on
Comment #5957 by Johan on
Comment #5986 by Kevin Buzzard on
Comment #5988 by Pieter Belmans on
Comment #5990 by Johan on
Comment #6018 by Harry Gindi on
Comment #6025 by Kevin Buzzard on
There are also: