Say we have two sheaves A and B and a homomorphism defined for each U: $\phi(U)$: A(U) $\rightarrow$ B(U) where A(U)= sections of A defined on U
Say we define $h^{-1}(A)= \lim_{h(U) \subset V} A(V)$.
There is supposed to be an induced homomorphism of sheaves $\phi_h: h^{-1}(A) \rightarrow h^{-1}(B)$. How to show that this is a well defined induced map??