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Brown representability often fails for homotopy categories of complexes
Brown representability Adjoint functor Triangulated cate-gory
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2011/2/22
We show that for the homotopy category K(Ab) of com-plexes of abelian groups, both Brown representability and Brown repre-sentability for the dual fail. We also provide an example of a localizing subc...
Failure of Brown representability in derived categories
Brown representability derived categories
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2010/10/29
Let T be a triangulated category with coproducts, C the full subcategory of compact objects in T. If T is the homotopy category of spectra, Adams proved the following in [Adams71]: All contravariant ...