We consider category of sheaf of $SpecA$.$O_{SpecA}$-Mod represents the sheaf of module. There is a natural forgetful functor $U$ from the sheaf of modules to $Sh(SpecA)$.this is a exact functor.
- I wonder is there another functor from $Sh(SpecA)$ to the sheaf of modules such that it is the left adjoint of $U$?
I think in general,this is not right.for any sheaf $F$,there exists a $A$ module $M$ such that $F=M$~ maybe ridiculous. If $U$ don't have left adjoint,this is also interesting!
- is there some particular ring make this true?