Let $f:X\rightarrow Y$ be a local homeomorphism. How should I show that the inverse image functor $f^*: Sh(Y) \rightarrow Sh(X)$ has a left adjoint?
I think it is because when we have a local homeomorphism, a sheaf $F$ on $X$ and $G$ on $Y$ then $f^{-1}(G)$ will be a sheaf itself and it does not need shifification.... but to be honest I have no idea to prove this....