On the Brown representability theorem for triangulated categories

By J. Franke. 2001

52 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2aa6e3d575fe5be7dc0001e69f4e79b69dbed528

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In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Generalized Brown representability in homotopy categories (2005, unknown): “Brown representability theorems for cohomology for triangulated categories are considered in [16], [35] and [29].”
Failure of Brown representability in derived categories (2000, background): “The best and most recent results were obtained independently by Franke [16] and Neeman [38], and one of the remarkable aspects of their theorems, is that they prove new results even in homotopy theory.”
Approximations and adjoints in homotopy categories (2010, background): “It is a well-known fact that the derived category of any Grothendieck abelian category has small Hom-sets [3, 5, 15].”
Triangulated Categories: Localization theory for triangulated categories (2008, unknown): “.10. Notes. The Brown representability theorem in homotopy theory is due to Brown [9]. Generalizations of the Brown representability theorem for triangulated categories can be found in work of Franke [13], Keller [21], and Neeman [31, 33]. The version used here is taken from [24]. The ﬁnite localiza”
Cohomological quotients and smashing localizations (2003, methodology): “Next we recall from [21] a variant of Brown’s Representability Theorem [6]; see also [16, 27, 8].”
Isomorphisms between left and right adjoints (2002, unknown): “A main point of Neeman’s later monograph [26] and of Franke’s paper [9] is to replace compact detection by a weaker notion that makes use of cardinality considerations familiar from the theory of Bousfield localization in algebraic topology.”
Derived equivalences from mutations of quivers with potential (2009, background): “udocompact derived category of A by Dpc(A) = D(Pcm(A)). Notice that the opposite category Dpc(A)op is isomorphic to D(Pcm(A)op) and that Pcm(A)op is a locally ﬁnite Grothendieck category. As shown in [17], cf. also [26], the category of complexes over a Grothendieck category admits a structure of Qu”
Hochschild cohomology of abelian categories and ringed spaces (2004, methodology): “In this section we construct a generalization of the usual injective model structure on C(C) [1, 6, 11].”
On differential graded categories (2006, background): “[51], [151], [71]) is a localization of D(A) and thus is well-generated.”