## 54 Citations

COMODULES AND CONTRAMODULES

- MathematicsGlasgow Mathematical Journal
- 2010

Abstract Algebras A and coalgebras C over a commutative ring R are defined by properties of the (endo)functors A ⊗R – and C ⊗R – on the category of R-modules R. Generalising these notions, monads and…

Galois functors and generalised Hopf modules

- Mathematics
- 2013

As shown in a previous paper by the same authors, the theory of Galois functors provides a categorical framework for the characterisation of bimonads on any category as Hopf monads and also for the…

Adjunctions of Hom and Tensor as Endofunctors of (Bi-)Module Categories Over Quasi-Hopf Algebras

- Mathematics
- 2014

For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor functors − ⊗ k V and V ⊗ k − are known to be left adjoint to some kind of Hom-functors as endofunctors of H 𝕄. The…

Hom-Tensor Relations for Two-Sided Hopf Modules Over Quasi-Hopf Algebras

- Mathematics
- 2012

For a Hopf algebra H over a commutative ring k, the category of right Hopf modules is equivalent to the category 𝕄 k of k-modules, that is, the comparison functor is an equivalence (Fundamental…

Categories of modules, comodules and contramodules over representations

- Mathematics
- 2021

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As…

Cofree objects in the categories of comonoids in certain abelian monoidal categories

- Mathematics
- 2016

We investigate cofree coalgebras, and limits and colimits of coalgebras in some abelian monoidal categories of interest, such as bimodules over a ring, and modules and comodules over a bialgebra or…

NOTES ON BIMONADS AND HOPF MONADS

- Mathematics
- 2010

For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguieres and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads). In a recent…

ON BIMONADS AND HOPF MONADS

- Mathematics
- 2012

For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguières and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads). In a recent…

Bimonads and Hopf monads on categories

- Mathematics
- 2007

The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector…

## References

SHOWING 1-10 OF 63 REFERENCES

The Structure of Corings: Induction Functors, Maschke-Type Theorem, and Frobenius and Galois-Type Properties

- Mathematics
- 2000

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 separable. We then…

Bimonads and Hopf monads on categories

- Mathematics
- 2007

The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector…

Algebras Versus Coalgebras

- MathematicsAppl. Categorical Struct.
- 2008

This survey is to show the connection between results from different fields and to trace a number of them back to some fundamental papers in category theory from the early 1970s, to look at the interplay between algebraic and coalgebraic notions.

TRIPLES, ALGEBRAS AND COHOMOLOGY

- Mathematics
- 1967

It is with great pleasure that the editors of Theory and Applications of Categories make this dissertation generally available. Although the date on the thesis is 1967, there was a nearly complete…

Homological Algebra of Semimodules and Semicontramodules

- Mathematics
- 2007

We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call…

Compatibility Conditions Between Rings and Corings

- Mathematics
- 2009

We introduce the notion of “bi-monoid” in general monoidal category, generalizing by this the notion of “bialgebra”. In the case of bimodules over a noncommutative algebra, we obtain compatibility…

Equivalences between categories of modules and categories of comodules

- Mathematics
- 2006

We show the close connection between apparently different Galois theories for comodules introduced recently in [J. Gómez-Torrecillas and J. Vercruysse, Comatrix corings and Galois Comodules over firm…

Homological algebra of semimodules and semicontramodules. Semi-infinite homological algebra of assoc

- Mathematics
- 2007

Preface.- Introduction.- 0 Preliminaries and Summary.- 1 Semialgebras and Semitensor Product.- 2 Derived Functor SemiTor.- 3 Semicontramodules and Semihomomorphisms.- 4 Derived Functor SemiExt.- 5…