Hopf Monads: A Survey with New Examples and Applications

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2023-08-27 DOI:10.1007/s10485-023-09732-1

Aryan Ghobadi

引用次数: 0

Abstract

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.

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Hopf单子:新例子和应用综述

本文综述了一元范畴上的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叉积理论，以及Hopf代数基本定理和Hopf代数的Radford双积定理的类似物。此外，我们还描述了由双代数的伽罗瓦和奥尔扩展产生的Hopf单子的新例子。我们还对集合和函数范畴上相应的单子变成Hopf的Lawvere理论以及自然数偏序集上的Hopf单子进行了分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.