International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 4, Pages 203-225
doi: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 J. Gómez-Torrecillas. 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.