Exactness of the double dual and Morita duality for Grothendieck categories

DOI10.1016/0021-8693(83)90166-7zbMath0524.16014OpenAlexW1968287584MaRDI QIDQ585336

Robert R. Colby, Kent R. Fuller

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0021-8693(83)90166-7

zbMATH Keywords

Grothendieck categoryinjective envelopeexact functorsquotient categoriesMorita dualitycategory of right modulesdouble dual functorsleft QF-3localizing subcategoriestorsion modules

Mathematics Subject Classification ID

Related Items (13)

Nakayama's conjecture and the double dual functors ⋮ Endomorphism rings with morita duality ⋮ On the heart of a faithful torsion theory ⋮ On duality theory and \(AB5^*\) modules ⋮ Morita duality emerging from quasi-abelian categories ⋮ QF-3 rings and morita duality ⋮ Relative QF-3' modules and QF-3 modules ⋮ Comatrix Coring Generalized and Equivalences of Categories of Comodules ⋮ Linear compactness and Morita duality for Grothendieck categories ⋮ Morita Duality for Grothendieck Categories with Applications to Coalgebras ⋮ On rings whose double dual functors preserve monomorphisms ⋮ Adjoint and Frobenius Pairs of Functors for Corings ⋮ Morita dualities associated with the \(R\)-dual functors

Cites Work

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• Duality in QF-3 rings
• A generalization of quasi-Frobenius rings
• Localizations in categories of modules. I
• On left \(QF-3\) rings
• Modules with decompositions that complement direct summands
• Exactness of the Double Dual
• On morita duality for additive group valued functors
• Completely Faithful Modules and Self-Injective Rings
• A Generalization of Quasi-Frobenius Rings
• The Structure of QF-3 Rings

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