Suppleness of the sheaf of algebras of generalized functions on   manifolds
  We show that the sheaves of algebras of generalized functions $\Omega\to \mathcal{G}(\Omega)$ and $\Omega\to \mathcal{G}^{\infty}(\Omega)$, $\Omega$ are open sets in a manifold $X$, are supple, contrary to the non-suppleness of the sheaf of distributions. 
Stevan Pilipovic and Milica Zigic
math.FA