Criteria for the injectivity of analytic sheaves

It is shown that a module $\mathscr{L}$ over the sheaf $\mathscr{O}$ of germs of holomorphic functions on a domain $G$ of $\mathbf{C}^n$ is injective if and only if the following conditions are satisfied; a) $\mathscr{L}$ is flabby; b) for every closed set $S\subset G$ and every point $z\in G$, the stalk $S^{l}_z$ of the sheaf $S^{\mathscr{L}}: U\mapsto\Gamma_S(U:\mathscr{L})$ is an injective $\mathscr{O}_z$-module. It follows in particular that the sheaf of germs of hyperfunctions is injective over the sheaf of germs of analytic functions.