Hopf Monads: A Survey with New Examples and Applications
Hopf Monads: A Survey with New Examples and Applications
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Hopf Monads：新示例和应用的调查
DOI：
10.1007/s10485-023-09732-1
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发表时间：
2023
影响因子：
0.6
通讯作者：
Ghobadi A
中科院分区：
文献类型：
--
作者：
Ghobadi A
本文综述了monoidal范畴上的Hopf单子理论，并给出了新的例子和应用。作为应用，我们利用这一机制提出了一个新的理论的交叉产品，以及类似物的基本定理的Hopf代数和拉德福的双积定理的Hopf代数体。此外，我们描述了源自双代数的伽罗瓦和奥尔扩展的霍普夫单子的新例子。我们还分类Lawvere理论，其相应的单子的类别的集合和功能成为霍普夫，以及霍普夫单子偏序集的自然数。
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.