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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 4, Pages 203-225
http://dx.doi.org/10.1155/S016117120201270X

Separable functors in corings

Departamento de Álgebra, Universidad de Granada, Granada E18071, Spain

Received 5 April 2001; Revised 25 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We develop some basic functorial techniques for the study of the categories of comodules over corings. In particular, we prove that the induction functor stemming from every morphism of corings has a left adjoint, called ad-induction functor. This construction generalizes the known adjunctions for the categories of Doi-Hopf modules and entwined modules. The separability of the induction and ad-induction functors are characterized, extending earlier results for coalgebra and ring homomorphisms, as well as for entwining structures.