论文标题
HOPF MONADS：一项带有新示例和应用的调查
Hopf Monads: A Survey with New Examples and Applications
论文作者
论文摘要
我们调查了Hopf Monads在单体类别上的理论，并提出了新的示例和应用。作为应用程序，我们利用这种机械来提出跨产品的新理论，以及Hopf代数和Radford的Hopf代数定理的基本定理的类似物。此外，我们描述了由Galois和Bialgebras的矿石扩展产生的Hopf Monad的新例子。我们还对律师理论进行了分类，其在集合和功能类别上的相应单调变成了Hopf，以及自然数量的hopf monads。
We survey the theory of Hopf monads on monoidal categories, and present new examples and applications. As applications, we utilise this machinery to present a new theory of cross products, as well as analogues of the Fundamental Theorem of Hopf algebras and Radford's biproduct Theorem for Hopf algebroids. Additionally, we describe new examples of Hopf monads which arise from Galois and Ore extensions of bialgebras. We also classify Lawvere theories whose corresponding monads on the category of sets and functions become Hopf, as well as Hopf monads on the poset of natural numbers.
