Homology of sheaves via Brown representability

Brown representability and the Eilenberg-Watts theorem in homotopical algebra

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-2014-12423-3 ◽

2014 ◽

Vol 143 (5) ◽

pp. 2269-2279

Author(s):

Mark Hovey

Keyword(s):

Homotopical Algebra ◽

Brown Representability

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Brown Representability and Spaces over a Category

Revista Colombiana de Matemáticas ◽

10.15446/recolma.v48n1.45195 ◽

2014 ◽

Vol 48 (1) ◽

pp. 55-77

Author(s):

Noé Bárcenas

Keyword(s):

Brown Representability

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The dual of the homotopy category of projective modules satisfies Brown representability

Bulletin of the London Mathematical Society ◽

10.1112/blms/bdu039 ◽

2014 ◽

Vol 46 (4) ◽

pp. 765-770 ◽

Cited By ~ 1

Author(s):

George Ciprian Modoi

Keyword(s):

Homotopy Category ◽

Projective Modules ◽

Brown Representability

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On the Brown representability theorem for triangulated categories

Topology ◽

10.1016/s0040-9383(99)00034-8 ◽

2001 ◽

Vol 40 (4) ◽

pp. 667-680 ◽

Cited By ~ 14

Author(s):

Jens Franke

Keyword(s):

Triangulated Categories ◽

Brown Representability

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Brown representability often fails for homotopy categories of complexes

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is011010026jkt167 ◽

2011 ◽

Vol 9 (1) ◽

pp. 151-160 ◽

Cited By ~ 3

Author(s):

George Ciprian Modoi ◽

Jan Šťovíček

Keyword(s):

Abelian Groups ◽

Homotopy Category ◽

Brown Representability ◽

Localizing Subcategory

AbstractWe show that for the homotopy categoryK(Ab) of complexes of abelian groups, both Brown representability and Brown representability for the dual fail. We also provide an example of a localizing subcategory ofK(Ab) for which the inclusion intoK(Ab) does not have a right adjoint.

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