The Structure of Weak Coalgebra-galois Extensions
نویسندگان
چکیده
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.
منابع مشابه
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.
متن کاملLocally 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...
متن کاملMorita Theory for Coring Extensions and Cleft Bicomodules
A Morita context is constructed for any comodule of a coring and, more generally, for an L-C bicomodule Σ for a coring extension (D : L) of (C : A). It is related to a 2-object subcategory of the category of k-linear functors M → M. Strictness of the Morita context is shown to imply the Galois property of Σ as a C-comodule and a Weak Structure Theorem. Sufficient conditions are found also for a...
متن کاملA History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...
متن کامل2 3 Ju n 20 06 AN EXPLICIT FORMULA FOR A STRONG CONNECTION
An explicit formula for a strong connection form in a principal extension by a coseparable coalgebra is given. 1. In the studies of geometry of non-commutative principal bundles or coalgebraGalois extensions (cf. [7]) an important role is played by the notion of a strong connection (for the universal differential structure) first introduced in the context of Hopf-Galois extensions in [10]. The ...
متن کامل