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 investigate adjoint and Frobenius pairs between categories of comodules over rather
general corings. We particularize to the case of the adjoint pair of functors associated to a …

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-
module an A-coring is associated. This new coring is termed a base ring extension of a …

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 study the various categories of corings, coalgebras, and comodules from a categorical
perspective. Emphasis is given to the question which properties of these categories can be …

In this article we defined and studied quasi-finite comodules, the cohom functors for
coalgebras over rings. Linear functors between categories of comodules are also …

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 …

By a theorem due to Kato and Ohtake, any (not necessarily strict) Morita context induces an
equivalence between appropriate subcategories of the module categories of the two rings in …

Let 𝕂 be a comonad on a model category M. We provide conditions under which the
associated category M𝕂 of 𝕂‐coalgebras admits a model category structure such that the …

INTRODUCTION wx In 8, K. Morita introduced a useful notion of duality between categories
of modules, usually called ''Morita duality.''He proved that every duality is given by …