Hi All, I am new to this chat room, but I have come upon a question that I'm sure someone here can answer. I am in a situation where I have a manifold M (with boundary), and three (pre)-sheaves of L_\infty algebras on M; let's call them A,B,C, and they fit into a diagram (with all maps strictly intertwining brackets) A\to C\leftarrow B. I further know that A,B, and C satisfy Čech descent (i.e. the natural map from the Čech complex for a cover of U to A(U) is a quasi-isomorphism) for arbitrary covers. And I know that the map B\to C is, open by open, surjective. I would like to say that this …