The Brown representability theorem and phantomless triangulated categories

DOI10.1016/0021-8693(92)90135-9zbMath0799.18006OpenAlexW2083851323MaRDI QIDQ1204556

Amnon Neeman

Publication date: 29 March 1993

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(92)90135-9

zbMATH Keywords

triangulated categoryderived categoryhomological functorrepresentable functorsphantom phenomena

Mathematics Subject Classification ID

Homological algebra in category theory, derived categories and functors (18G99)

Related Items (23)

Higher ideal approximation theory ⋮ Approximable triangulated categories ⋮ The phantom cover of a module. ⋮ Triangulated categories and the Ziegler spectrum ⋮ On Covers and Envelopes in Some Functor Categories ⋮ Gorenstein homological algebra and universal coefficient theorems ⋮ Gorenstein flat phantom morphisms ⋮ Higher phantom and Ext-phantom morphisms ⋮ A local-global principle for small triangulated categories ⋮ Completing perfect complexes. With appendices by Tobias Barthel and Bernhard Keller ⋮ Ideal approximation theory ⋮ From Ohkawa to Strong Generation via Approximable Triangulated Categories—A Variation on the Theme of Amnon Neeman’s Nagoya Lecture Series ⋮ Phantom ideals and cotorsion pairs in extriangulated categories ⋮ Covering ideals of morphisms and module representations of the quiver \(\mathbb A_2\). ⋮ Relative homological algebra and purity in triangulated categories ⋮ Higher phantom morphisms with respect to a subfunctor of ext ⋮ On \(n\)-phantom and \(n\)-ext-phantom morphisms ⋮ Neat-phantom and clean-cophantom morphisms ⋮ Stable homotopy as a triangulated functor ⋮ Powers of the phantom ideal ⋮ Precovers and Preenvelopes by Phantom and Ext-Phantom Morphisms ⋮ Phantom envelopes and Ext-phantom covers of modules ⋮ Rd-phantom and RD-Ext-phantom morphisms

Cites Work

• Some new axioms for triangulated categories
• Cohomology theories
• Equivariant stable homotopy theory. With contributions by J. E. McClure
• The derived category of an exact category
• Stable homotopy as a triangulated functor
• \(K\)-theory for triangulated categories. I(B): Homological functors
• A variant of E. H. Brown's representability theorem
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