Morita theory for coring extensions and cleft bicomodules

15Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

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 MC → MD. 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 Strong Structure Theorem to hold. Cleft property of an L - C bicomodule Σ-implying strictness of the associated Morita context-is introduced. It is shown to be equivalent to being a GaloisC -comodule and isomorphic to EndC (Σ) ⊗L D, in the category of left modules for the ring EndC (Σ) and right comodules for the coring D, i.e. satisfying the normal basis property. Algebra extensions, that are cleft extensions by a Hopf algebra, a coalgebra or a Hopf algebroid, as well as cleft entwining structures (over commutative or non-commutative base rings) and cleft weak entwining structures, are shown to provide examples of cleft bicomodules. © 2006 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Böhm, G., & Vercruysse, J. (2007). Morita theory for coring extensions and cleft bicomodules. Advances in Mathematics, 209(2), 611–648. https://doi.org/10.1016/j.aim.2006.05.010

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free