Henning Krause

摘要

Auslander's formula shows that any abelian category $mathsf C$ is equivalent to the category of coherent functors on $mathsf C$ modulo the Serre subcategory of all effaceable functors. We establish a derived version of this equivalence. This amounts to showing that the homotopy category of injective objects of some appropriate Grothendieck abelian category (the category of ind-objects of $mathsf C$) is compactly generated and that the full subcategory of compact objects is equivalent to the bounded derived category of $mathsf C$. The same approach shows for an arbitrary Grothendieck abelian category that its derived category and the homotopy category of injective objects are well-generated triangulated categories. For sufficiently large cardinals $lpha$ we identify their $lpha$-compact objects and compare them.