Dual Entwining Structures and Dual Entwined Modules

Abuhlail, Jawad

doi:10.1007/s10468-005-3605-4

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…We will now give conditions for the functor G : Mod − R −→ Mod C R to be separable. Since G has a left adjoint, it follows (see [27,Theorem 1.2]) that G is separable if and only if there exists a natural transformation ω ∈ N at (1…”

Section: Proofmentioning

confidence: 99%

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Entwined Modules Over Representations of Categories

Banerjee

2023

Algebr Represent Theor

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We introduce a theory of modules over a representation of a small category taking values in entwining structures over a semiperfect coalgebra. This takes forward the aim of developing categories of entwined modules to the same extent as that of module categories as well as the philosophy of Mitchell of working with rings with several objects. The representations are motivated by work of Estrada and Virili, who developed a theory of modules over a representation taking values in small preadditive categories, which were then studied in the same spirit as sheaves of modules over a scheme. We also describe, by means of Frobenius and separable functors, how our theory relates to that of modules over the underlying representation taking values in small K -linear categories.

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Section: Proofmentioning

confidence: 99%

“…r in R x and c ∈ C. There is a canonical morphism N at(1 Mod−R , F G ) −→ W 1 . Proof As mentioned above, any ω ∈ N at(1 Mod−R , F G ) corresponds to a collection of natural transformations {ω x ∈ N at(1 M R x , F x G x )} x∈X satisfying(8.1).…”

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confidence: 99%

Entwined Modules Over Representations of Categories

Banerjee

2023

Algebr Represent Theor

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Entwined modules over linear categories and Galois extensions

2021

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In this paper, we study modules over quotient spaces of certain categorified fiber bundles. These are understood as modules over entwining structures involving a small K-linear category D and a K-coalgebra C. We obtain Frobenius and separability conditions for functors on entwined modules. We also introduce the notion of a C-Galois extension E ⊆ D of categories. Under suitable conditions, we show that entwined modules over a C-Galois extension may be described as modules over the subcategory E of C-coinvariants of D.

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Duality theorems for crossed products over rings

Abuhlail

2005

Journal of Algebra

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In this paper we improve and extend duality theorems for crossed products obtained by M. Koppinen (C. Chen) from the case of base fields (Dedekind domains) to the case of arbitrary Noetherian commutative ground rings under fairly weak conditions. In particular we extend an improved version of the celebrated Blattner-Montgomery duality theorem to the case of arbitrary Noetherian commutative ground rings.  2005 Elsevier Inc. All rights reserved.

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Dual Entwining Structures and Dual Entwined Modules

Abstract: In this note we introduce and investigate the concepts of dual entwining structures and dual entwined modules. This generalizes the concepts of dual Doi-Koppinen structures and dual Doi-Koppinen modules introduced (in the infinite case over rings) by the author is his dissertation.

Cited by 4 publications

References 17 publications

Entwined Modules Over Representations of Categories

Entwined Modules Over Representations of Categories

Entwined modules over linear categories and Galois extensions

Duality theorems for crossed products over rings

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