On Neeman's well generated triangulated categories

By Henning Krause. Documenta Mathematica, 2001

72 citations recorded by the source corpus.

We characterize Neeman's well generated triangulated categories and discuss some of its basic properties.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/3c3a9f92159bf999d834848cf91e66c2c3fd80d2

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Citations in the corpus

Totally acyclic complexes over noetherian schemes (2009, background): “For material on well-generated triangulated categories, see [Nee01, Kra01 , Kra07].”
Triangulated Categories: Localization theory for triangulated categories (2008, unknown): “lated were introduced and studied by Neeman in his book [33] as a natural generalization of compactly generated triangulated categories. For an alternative approach which simpliﬁes the deﬁnition, see [23]. More recently, well generated categories with speciﬁc models have been studied; see [37, 47] f”
Microlocal Morse theory of wrapped Fukaya categories (2018, background): “Theorem A.3 also holds under the weaker hypothesis that C is well generated rather than compactly generated, by work of Neeman adapted to the dg/A∞ case (for a definition of this notion see [40, §8], and for a proof of Theorem A.3 in that setting, see [40, Prop.”
Generalized Brown representability in homotopy categories (2005, unknown): “Krause [29] to perfectly generated triangulated categories; in [30] he compares his perfect generation with the well generation of Neeman.”
A universal characterization of higher algebraic K-theory (2010, background): “an’s generalization of Thomason’s localization theorem (see [61, 4.4.9] or [62]) to show that the left vertical map is fully faithful. First, since Indκ(A) and Indκ(B) are presentable, the criterionof[50](characterizingwell-generatedtriangulatedcategories)and[53, 1.4.5.2] imply that Ho(Indκ(B)) is w”
On differential graded categories (2006, background): “A triangulated category T is well-generated [112], [94] if it admits arbitrary coproducts and a good set of generators G, i.”
A tour about existence and uniqueness of dg enhancements and lifts (2016, background): “The interested reader can find a very nice survey in [36], where Neeman’s original theory (see [47]) is revisited with the point of view of [35].”