Let X$X$ be an arbitrary scheme. A quasi coherent sheaf \cal F$\cal F$ is said to be injective if Hom_{ O_X}(-, \cal F)$Hom_{ O_X}(-, \cal F)$ is exact. We can also regard a quasi coherent sheaf \cal G$\cal G$ on X$X$ such that for all open subset U$U$ of X$X$, \cal G(U)$\cal G(U)$ is an injective \cal O_X$\cal O_X$-module. So we can ask a question that
1)Is there any relation between these tow kind of sheaves?
2)Which conditions on X (or on\cal F) are needed to regard the first kink of these sheaves (\cal F) equivalent to the second one?
Is there any relation between these two kind of sheaves?
Which conditions on $X$ (or on $\cal F$) are needed to regard the first kind of these sheaves ($\cal F$) equivalent to the second one?
