Given a ring A and an A-coring C, we study when the forgetful functor from the category of
right C-comodules to the category of right A-modules and its right adjoint−⊗ AC are …

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 …

We study the corings whose category of right comodules has a finitely generated projective
generator. In order to extricate the structure of these corings, we introduce the notion of …

El Kaoutit and Gómez-Torrecillas introduced comatrix corings, generalizing Sweedler's
canonical coring, and proved a new version of the Faithfully Flat Descent Theorem. They …

We study the following question: when is the right adjoint of the forgetful functor from the
category of $(H, A, C) $-Doi-Hopf modules to the category of $ A $-modules also a left …

Let A be a ring and MA the category of right A-modules. It is well known in module theory
that any A-bimodule B is an A-ring if and only if the functor−⊗ AB: MA→ MA is a monad (or …

We show that the well-known Morita theorems on equivalences of categories of modules
hold true of categories of comodules over a field k. We go parallel with| H. Bass, Algebraic K …

We investigate functors between abelian categories having usomor-phic left and right
adjoint functors (these functors are called Frobenius Functors). They are characterized for …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

For a given entwining structure (A, C) ψinvolving an algebraA, a coalgebraC, and an
entwining map ψ: C⊗ A→ A⊗ C, a categoryMCA (ψ) of right (A, C) ψ-modules is defined and …