### Abstract

Interpreting Hopf algebras and their various generalizations as Hopf monads begins in this chapter with classical Hopf algebras over fields. Endofunctors on the category of vector spaces are considered, which are induced by taking the tensor product with a fixed vector space. The algebra structures on this vector space are related to the monad structures on the induced functor; and the coalgebra structures are related to the opmonoidal structures. This results in a bijection between the bialgebras; and the induced bimonads on the category of vector spaces. The bijection is shown to restrict to Hopf algebras on one hand; and Hopf monads on the other hand.

Original language | English |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 47-58 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Jan 1 2018 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2226 |

ISSN (Print) | 0075-8434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Böhm, G. (2018). (Hopf) bialgebras. In

*Lecture Notes in Mathematics*(pp. 47-58). (Lecture Notes in Mathematics; Vol. 2226). Springer Verlag. https://doi.org/10.1007/978-3-319-98137-6_4