Adjoint functors and equivalences of subcategories

DOI10.1016/S0007-4497(03)00043-5zbMath1029.18003OpenAlexW2023751357MaRDI QIDQ1407224

Florencio Castaño Iglesias, Robert Wisbauer, José Gómez-Torrecillas

Publication date: 15 September 2003

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0007-4497(03)00043-5

zbMATH Keywords

comodulesadjoint functorsequivalence of categoriesMorita theory

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Abelian categories, Grothendieck categories (18E10) Categories admitting limits (complete categories), functors preserving limits, completions (18A35) Homological dimension in associative algebras (16E10) Artinian rings and modules (associative rings and algebras) (16P20)

Related Items (10)

D4-objects in abelian categories: Transfer via functors ⋮ Rickart and dual Rickart objects in abelian categories: transfer via functors ⋮ Transfer of CS-Rickart and dual CS-Rickart properties via functors between Abelian categories ⋮ Localizations, colocalizations and non additive \(\ast\)-objects ⋮ Pure-direct-objects in categories: transfer via functors ⋮ Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories ⋮ On a Natural Duality Between Grothendieck Categories ⋮ Baer-Kaplansky classes in categories: transfer via functors ⋮ Strongly Rickart objects in abelian categories ⋮ Idempotent monads and \(\star \)-functors

Cites Work

• Static modules and stable Clifford theory
• Hopf-Galois extensions of algebras, the Miyashita-Ulbrich action, and Azumaya algebras
• Static modules, stable Clifford theory, and Morita similarities of rings
• On equivalences between module subcategories
• Separable functors in graded rings
• On the structure of *-modules
• Stable Clifford theory for divisorially graded rings
• Comatrix corings: Galois corings, descent theory, and a structure theorem for cosemisimple corings.
• Cointegrations, relative cohomology for comodules, and coseparable corings
• The structure of corings: induction functors, Maschke-type theorem, and Frobenius and Galois-type properties
• Morita theory for corings and cleft entwining structures.
• Some remarks on equivalences between categories of modules
• Tilting in Grothendieck categories
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