Titlebook: Hopf Algebras and Their Generalizations from a Category Theoretical Point of View; Gabriella B?hm Book 2018 Springer Nature Switzerland AG

尊重

戰(zhàn)勝

(Hopf) Bialgebroids,eplaced by the category of bimodules over some algebra .; or, isomorphically, the category of left modules over .???... Those endofunctors on it are considered which are induced, as in Example . 4, by the .???..-module tensor product with a fixed .???..-bimodule .. The monad structures on this funct

CROW

Brochure

(Hopf) Bimonoids in Duoidal Categories, the morphisms in the category and all natural transformations between the induced functors. Those monads are identified which correspond to monoids; and those opmonoidal functors are identified which correspond to comonoids. This leads to an equivalence between bimonoids in a duoidal category and b

Mendicant

glamor

修剪過(guò)的樹(shù)籬

(Hopf) Bialgebras,. 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.

鞭打

Host142

Introduction,eneralizations of Hopf algebra as Hopf monad structures on suitable functors. The covered examples include classical Hopf algebras, Hopf monoids in duoidal (in particular braided monoidal) categories, Hopf algebroids and (in particular) weak Hopf algebras.

Meditate

(Hopf) Bimonads,ient and necessary condition is obtained for the lifting of the closed structure as well, in the form of the invertibility of a canonical natural transformation. A Hopf monad is defined as a bimonad for which this natural transformation is invertible.