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.
- Pub Date:
- May 2013
- Mathematics - Category Theory;
- Mathematics - Algebraic Geometry;
- First version: preliminary version, comments are welcome! Second version: An (important) error was removed, some details were added. Comments are also welcome! Third version: a new application is added, some typos are removed. Fourth version: final version, some important corrections are made, to appear in Arkiv Math