Deriving Auslander's Formula

Krause H (2015)
Documenta Mathematica 20: 669-688.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Auslander's formula shows that any abelian category C is equivalent to the category of coherent functors on 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 C) is compactly generated and that the full subcategory of compact objects is equivalent to the bounded derived category of 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 alpha we identify their alpha-compact objects and compare them.
Erscheinungsjahr
2015
Zeitschriftentitel
Documenta Mathematica
Band
20
Seite(n)
669-688
ISSN
1431-0643
Page URI
https://pub.uni-bielefeld.de/record/2901266

Zitieren

Krause H. Deriving Auslander's Formula. Documenta Mathematica. 2015;20:669-688.
Krause, H. (2015). Deriving Auslander's Formula. Documenta Mathematica, 20, 669-688.
Krause, H. (2015). Deriving Auslander's Formula. Documenta Mathematica 20, 669-688.
Krause, H., 2015. Deriving Auslander's Formula. Documenta Mathematica, 20, p 669-688.
H. Krause, “Deriving Auslander's Formula”, Documenta Mathematica, vol. 20, 2015, pp. 669-688.
Krause, H.: Deriving Auslander's Formula. Documenta Mathematica. 20, 669-688 (2015).
Krause, Henning. “Deriving Auslander's Formula”. Documenta Mathematica 20 (2015): 669-688.

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arXiv: 1409.7051

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