Corings and comodules

Brzeziński, Tomasz; Wisbauer, Robert

doi:10.1017/cbo9780511546495.005

Cited by 62 publications

(147 citation statements)

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“…For any discrete right S-module L, any left S-contramodule C, and any abelian group V there is a natural isomorphism (19) Hom Z (L ⊙ S C, V ) ∼ = Hom S (C, Hom Z (L, V )), (we recall that Hom S denotes the group of morphisms in the category of left S-contramodules S-contra).…”

Section: Morita Theory For Topological Ringsmentioning

confidence: 99%

The Tilting–Cotilting Correspondence

Positselski

Šťovíček

2019

International Mathematics Research Notices

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To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa. Then we construct an equivalence between the (conventional or absolute) derived categories of A and B. Under various assumptions on A, which cover a wide range of examples (for instance, if A is a module category or, more generally, a locally finitely presentable Grothendieck abelian category), we show that B is the abelian category of contramodules over a topological ring and that the derived equivalences are realized by a contramodule-valued variant of the usual derived Hom-functor.

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Section: Morita Theory For Topological Ringsmentioning

confidence: 99%

The Tilting–Cotilting Correspondence

Positselski

Šťovíček

2019

International Mathematics Research Notices

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“…Proof. Both statements are proved in exactly the same way as in the classical case of coalgebras over a field, see [BW,12.6,12.7].…”

Section: Lemma 1 Letmentioning

confidence: 73%

Coidempotent Subcoalgebras and Short Exact Sequences of Finitary 2-Representations

Chan¹,

Miemietz²

2020

Nagoya Math. J.

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“…∆(x) = g ⊗ x + x ⊗ h, for some g, h ∈ R. Later in [3], Brown et al extended Panov's result by allowing x to be more general. In this paper we extend Panov's characterisation to Ore extensions of weak Hopf algebras, where by weak Hopf algebras we mean a generalisation of Hopf algebras in the sense of Böhm et al [1] see also [4,7]. A weak Hopf algebra R is a (unital, associative) algebra and a (counital, coassociative) coalgebra, with counit ǫ and comultiplication ∆, satisfying certain conditions.…”

Section: Introductionmentioning

confidence: 95%

Panov’s theorem for weak Hopf algebras

Lomp¹,

Santana²,

Santos³

2019

Contemporary Mathematics

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Panov proved necessary and sufficient conditions to extend the Hopf algebra structure of an algebra R to an Ore extension R[x; σ, δ] with x being a skew-primitive element. In this paper we extend Panov's result to Ore extensions over weak Hopf algebras. As an application we study Ore extensions of connected groupoid algebras.The first author is a member of CMUP (UID/MAT/00144/2013), which is funded by FCT with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020.

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Corings and comodules

Cited by 62 publications

References 0 publications

The Tilting–Cotilting Correspondence

The Tilting–Cotilting Correspondence

Coidempotent Subcoalgebras and Short Exact Sequences of Finitary 2-Representations

Panov’s theorem for weak Hopf algebras

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