Deriving Auslander's formula

  • Henning Krause

    Fakultät für Mathematik Universität Bielefeld D-33501 Bielefeld Germany
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Auslander's formula shows that any abelian category is equivalent to the category of coherent functors on 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 ) is compactly generated and that the full subcategory of compact objects is equivalent to the bounded derived category of . 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 we identify their -compact objects and compare them.

Cite this article

Henning Krause, Deriving Auslander's formula. Doc. Math. 20 (2015), pp. 669–688

DOI 10.4171/DM/501