Deriving Auslander's formula (Q273513)

\textit{M. Auslander} [in: Proc. Conf. Categor. Algebra, La Jolla 1965, 189--231 (1966; Zbl 0192.10902)] showed that any abelian category \(\mathcal C\) is equivalent to the category of coherent functors on \(\mathcal C\) modulo the Serre subcategory of all effaceable functors. In the paper under review, the author establishes a derived version of Auslander's formula. He shows that the homotopy category of injective objects of some appropriate Grothendieck abelian category (the category of ind-objects of \(\mathcal C\)) is compactly generated and that the full subcategory of compact objects is equivalent to the bounded derived category of \(\mathcal C\). 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. Finally, the author identifies \(\alpha\)-compact objects and compare them, for sufficiently large cardinals \(\alpha\).