  Consider a complete abelian category which has an injective cogenerator. If
its derived category is left--complete we show that the dual of this derived
category satisfies Brown representability. In particular this is true for the
derived category of an abelian AB$4^*$-$n$ category, for the derived category
of quasi--coherent sheaves over a nice enough scheme (including the projective
finitely dimensional space) and for the full subcategory of derived category of
all sheaves over an algebraic stack consisting from complexes with
quasi--coherent cohomology.
