Milnor-Moore Categories and Monadic Decomposition

@article{Ardizzoni2014MilnorMooreCA,
  title={Milnor-Moore Categories and Monadic Decomposition},
  author={Alessandro Ardizzoni and Claudia Menini},
  journal={arXiv: Category Theory},
  year={2014}
}

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References

SHOWING 1-10 OF 53 REFERENCES

Monoidal Hom–Hopf Algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in

Categorical Constructions for Hopf Algebras

We prove that both the embedding of the category of Hopf algebras into that of bialgebras and the forgetful functor from the category of Hopf algebras to the category of algebras have right adjoints;

Quasi-bialgebra Structures and Torsion-free Abelian Groups

We describe all the quasi-bialgebra structures of a group algebra over a torsion-free abelian group. They all come out to be triangular in a unique way. Moreover, up to an isomorphism, these

CATEGORIES OF COMODULES AND CHAIN COMPLEXES OF MODULES

Let denote the coendomorphism left R-bialgebroid associated to a left finitely generated and projective extension of rings R → A with identities. We show that the category of left comodules over an

Adjunctions and braided objects

In this paper, we investigate the categories of braided objects, algebras and bialgebras in a given monoidal category, some pairs of adjoint functors between them and their relations. In particular,

Free Monoid in Monoidal Abelian Categories

TLDR
A conceptual explanation of the form of the free operad, free dioperad and free properad in monoidal abelian categories when the monoidal product does not necessarily preserve coproducts is given.
...