Semiseparable functors

DOI10.1016/j.jalgebra.2023.10.007arXiv2202.12113MaRDI QIDQ6087813

Alessandro Ardizzoni, Lucrezia Bottegoni

Publication date: 16 November 2023

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

Full work available at URL: https://arxiv.org/abs/2202.12113

zbMATH Keywords

bimodulesseparabilitycoringsEilenberg-Moore categories(co)reflections

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Eilenberg-Moore and Kleisli constructions for monads (18C20) Coalgebras and comodules; corings (16T15)

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Cites Work

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• Frobenius and separable functors for generalized module categories and nonlinear equations
• Idempotent monads and \(\star \)-functors
• Monads and comonads on module categories
• Separable functors applied to graded rings
• Separable functors in graded rings
• Torsion theories for coalgebras
• Separable functors in coalgebras. Applications
• Comatrix corings: Galois corings, descent theory, and a structure theorem for cosemisimple corings.
• Separable functors in corings
• The structure of corings: induction functors, Maschke-type theorem, and Frobenius and Galois-type properties
• Proper factorization systems in 2-categories
• Hopf modules, Frobenius functors and (one-sided) Hopf algebras
• Monadic decompositions and classical Lie theory
• A note on separable functors and monads with an application to equivariant derived categories
• Iterated wreath product of the simplex category and iterated loop spaces
• Hopf monads
• Naturally full functors in nature.
• Formally smooth bimodules.
• Adjoint functors and triples
• Separable functors revisited
• Galois theory for comatrix corings: Descent theory, Morita theory, Frobenius and separability properties
• Morita Theory for Comodules Over Corings
• The Predual Theorem to the Jacobson-Bourbaki Theorem
• Homological Algebra
• On Fundamental Constructions and Adjoint Functors
• Coreflective Subcategories