Injective module sheaves are flasque
= Injective module sheaves are flasque
For opens $U\subseteq V\subseteq X$, there is a monomorphism between the <extensions by zero> of $\mathcal O_U$ and $\mathcal O_V$. Morphisms from these sheaves into an <injective sheaf of modules> $I$ identify with sections on $U$ and $V$, respectively. The <injective object> extension property therefore makes the restriction $I(V)\to I(U)$ surjective, proving that $I$ is <flasque>. The argument applies to any <ringed space>.