The Structure of Weak Coalgebra-Galois Extensions

The Structure of Weak Coalgebra-galois Extensions

Weak coalgebra-Galois extensions are studied. A notion of an invertible weak entwining structure is introduced. It is proven that, within an invertible weak entwining structure, the surjectivity of the canonical map implies bijectivity provided the structure coalgebra C is either coseparable or projective as a C-comodule.

Locally coalgebra-Galois extensions

The paper introduces the notion of a locally coalgebra-Galois extension and, as its special case, a locally cleft extension, generalising concepts from [9]. The necessary and sufficient conditions for a locally coalgebra-Galois extension to be a (global) coalgebra-Galois extension are stated. As an important special case, it is proven, that under not very restrictive conditions the gluing of tw...

On Modules Associated to Coalgebra Galois Extensions

For a given entwining structure (A,C)ψ involving an algebra A, a coalgebra C, and an entwining map ψ : C ⊗ A → A ⊗ C, a category MA(ψ) of right (A,C)ψmodules is defined and its structure analysed. In particular, the notion of a measuring of (A,C)ψ to (Ã, C̃)ψ̃ is introduced, and certain functors between M C A(ψ) and M Ã (ψ̃) induced by such a measuring are defined. It is shown that these functors ...

Coalgebra-galois Extensions from the Extension Theory Point of View

Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a separable, split, or strongly separable extension.

Weak Compactness of the Set of ε-Extensions