A diagrammatic approach to Hopf monads
Category Theory
2010-03-15 v1 Quantum Algebra
Abstract
Given a Hopf algebra in a symmetric monoidal category with duals, the category of modules inherits the structure of a monoidal category with duals. If the notion of algebra is replaced with that of monad on a monoidal category with duals then Bruguieres and Virelizier showed when the category of modules inherits this structure of being monoidal with duals, and this gave rise to what they called a Hopf monad. In this paper it is shown that there are good diagrammatic descriptions of dinatural transformations which allows the three-dimensional, object-free nature of their constructions to become apparent.
Cite
@article{arxiv.0807.0658,
title = {A diagrammatic approach to Hopf monads},
author = {Simon Willerton},
journal= {arXiv preprint arXiv:0807.0658},
year = {2010}
}
Comments
26 pages, 170 diagrams