The Brown representability theorem and phantomless triangulated categories
نویسندگان
چکیده
منابع مشابه
Derived categories, resolutions, and Brown representability
These notes are based on a series of five lectures given during the summer school “Interactions between Homotopy Theory and Algebra” held at the University of Chicago in 2004.
متن کاملFailure of Brown Representability in Derived Categories
Let T be a triangulated category with coproducts, T ⊂ T the full subcategory of compact objects in T. If T is the homotopy category of spectra, Adams proved the following in [1]: All homological functors {T}op −→ Ab are the restrictions of representable functors on T, and all natural transformations are the restrictions of morphisms in T. It has been something of a mystery, to what extent this ...
متن کاملGeneralized Brown Representability in Homotopy Categories: Erratum
Propositions 4.2 and 4.3 of the author’s article (Theory Appl. Categ. 14 (2005), 451-479) are not correct. We show that their use can be avoided and all remaining results remain correct. Propositions 4.2 and 4.3 of the author’s [3] are not correct and I am grateful to J. F. Jardine for pointing it out. In fact, consider the diagram D sending the one morphism category to the point ∆0 in the homo...
متن کاملGeneralized Brown Representability in Homotopy Categories
Brown representability approximates the homotopy category of spectra by means of cohomology functors defined on finite spectra. We will show that if a model category K is suitably determined by λ-small objects then its homotopy category Ho(K) is approximated by cohomology functors defined on those λ-small objects. In the case of simplicial sets, we have λ = ω1, i.e., λ-small means countable.
متن کاملFailure of Brown Representability in Derived Categories
Let T be a triangulated category with coproducts, T ⊂ T the full subcategory of compact objects in T. If T is the homotopy category of spectra, Adams proved the following in [1]: All homological functors {T} −→ Ab are the restrictions of representable functors on T, and all natural transformations are the restrictions of morphisms in T. It has been something of a mystery, to what extent this ge...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1992
ISSN: 0021-8693
DOI: 10.1016/0021-8693(92)90135-9