f-morphism of sheaves
= f-morphism of sheaves
{c}
{title2=$\phi(U):\mathcal G(U)\to\mathcal F(f^{-1}U)$}
For a continuous map $f:X\to Y$, an f-morphism from a <sheaf> on $Y$ to a <sheaf> on $X$ is a family of the displayed maps commuting with restrictions. It is equivalently a <morphism of sheaves> $\mathcal G\to f_*\mathcal F$. For each $x\in X$ it induces a map $\mathcal G_{f(x)}\to\mathcal F_x$ on <stalks>, by pulling back the neighbourhood representing a <germ>.