Hopf Monads: A Survey with New Examples and Applications

被引：0

作者：

Ghobadi, Aryan ^{[1
]}

机构：

[1] Queen Mary Univ London, Sch Math, Mile End Rd, London E1 4NS, England

来源：

APPLIED CATEGORICAL STRUCTURES | 2023年 / 31卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Monads; Bimonads; Hopf algebras; Monoidal categories; Braided categories; Hopf algebroid; Bialgebroid; ALGEBRAS; EXTENSIONS; CATEGORIES; FUNCTORS;

D O I：

10.1007/s10485-023-09732-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：63

共 67 条

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