### Abstract

In this chapter an analysis is carried out which is analogous to, but more general than that in Chap. 4. The category of vector spaces in Chap. 4 is replaced by the category of bimodules over some algebra B; or, isomorphically, the category of left modules over B ⊗ B^{op}. Those endofunctors on it are considered which are induced, as in Example 2.5 4, by the B ⊗ B^{op}-module tensor product with a fixed B ⊗ B^{op}-bimodule A. The monad structures on this functor A⊗B⊗Bop− are related to the algebra homomorphisms B ⊗ B^{op} → A. The monoidal structure of the category of B-bimodules is explained in Example 3.2 5. The opmonoidal structures with respect to it on the endofunctor A⊗B⊗B^{op}−, are related to the so-called B|B-coring structures on A. This results in a bijection between the bimonads with underlying functor A⊗B⊗B^{op}− on the category of B-bimodules; and the bialgebroids over the base algebra B. The bijection is shown to restrict to Hopf monads on one hand; and Hopf algebroids on the other hand.

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

Publisher | Springer Verlag |

Pages | 59-73 |

Number of pages | 15 |

DOIs | |

Publication status | Published - Jan 1 2018 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2226 |

ISSN (Print) | 0075-8434 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Lecture Notes in Mathematics*(pp. 59-73). (Lecture Notes in Mathematics; Vol. 2226). Springer Verlag. https://doi.org/10.1007/978-3-319-98137-6_5