A Brown representability theorem via coherent functors

Krause H (2002)
Topology 41(4): 853-861.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper we discuss the Brown Representability Theorem for triangulated categories having arbitrary coproducts. This theorem is an extremely useful tool and various versions appear in the literature. All of them require a set of objects which generate the category in some appropriate sense. Depending on the proof, there are essentially two types: the first type is based on the analogue of iterated attaching of cells which is used in the topological case; the second type is based on solution sets and applies a variant of Freyd's Adjoint Functor Theorem. Motivated by recent work of Neeman (A. Neeman, Triangulated Categories, Annals of Mathematics Studies, 148, Princeton University Press, Princeton, NJ, 2001) and Franke (On the Brown representability theorem for triangulated categories, Topology, to appear), we prove a new theorem of the first type (Theorem A) and add, as an application, a Brown Representability Theorem for covariant functors (Theorem B). The final Theorem C establishes a filtration of a triangulated category which clarifies the relation between results of the first and the second type. (C) 2002 Elsevier Science Ltd. All rights reserved.
Stichworte
triangulated category; coherent functor; Brown representability
Erscheinungsjahr
2002
Zeitschriftentitel
Topology
Band
41
Ausgabe
4
Seite(n)
853-861
ISSN
0040-9383
Page URI
https://pub.uni-bielefeld.de/record/1614326

Zitieren

Krause H. A Brown representability theorem via coherent functors. Topology. 2002;41(4):853-861.
Krause, H. (2002). A Brown representability theorem via coherent functors. Topology, 41(4), 853-861. doi:10.1016/S0040-9383(01)00010-6
Krause, H. (2002). A Brown representability theorem via coherent functors. Topology 41, 853-861.
Krause, H., 2002. A Brown representability theorem via coherent functors. Topology, 41(4), p 853-861.
H. Krause, “A Brown representability theorem via coherent functors”, Topology, vol. 41, 2002, pp. 853-861.
Krause, H.: A Brown representability theorem via coherent functors. Topology. 41, 853-861 (2002).
Krause, Henning. “A Brown representability theorem via coherent functors”. Topology 41.4 (2002): 853-861.

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