Hopf Monads: A Survey with New Examples and Applications
Category Theory
2022-05-12 v1 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.2205.05310,
title = {Hopf Monads: A Survey with New Examples and Applications},
author = {Aryan Ghobadi},
journal= {arXiv preprint arXiv:2205.05310},
year = {2022}
}
Comments
59 pages. Comments are more than welcome!