The homotopy category of injectives

摘要

Krause studied the homotopy category K (InjA) of complexes of injectives in a locally noetherian Grothendieck abelian category A. Because A is assumed locally noetherian, we know that arbitrary direct sums of injectives are injective, and hence, the category K (InjA) has coproducts. It turns out that K (InjA) is compactly generated, and Krause studies the relation between the compact objects in K (InjA), the derived category D.A/, and the category Kac (InjA) of acyclic objects in K (InjA).