2013/05/26 by George Ciprian Modoi, Modoi, George Ciprian
Mathematics · #14F05 #16D90 #18E30 #55U35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1305.6028
openalex publication_date 2013/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 AB4^*-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.