Categorical Constructions for Hopf Algebras

Details Categorical Constructions for Hopf Algebras Categorical Constructions for Hopf Algebras

2009-05-16

arxiv.org/abs/0905.2613v3

Mathematics

Quantum Algebra

to appear in Communications in Algebra

Scientific paper

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; in other words: every bialgebra has a Hopf coreflection and on every algebra there exists a cofree Hopf algebra. In this way we give an affirmative answer to a forty years old problem posed by Sweedler. On the route the coequalizers and the coproducts in the category of Hopf algebras are explicitly described.

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