nopeJul 8, 2023
A diagrammatic approach to Hopf monads
(2008) : Willerton, Simon
DOI: https://doi.org/10.48550/arXiv.0807.0658
#formal_logic #hopf_algebra #hopf_monad #string_diagrams #diagram #my_bibtex
A diagrammatic approach to Hopf monads

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.

arXiv.org
nopeJun 2, 2022
A diagrammatic approach to Hopf monads
(2008) : Simon Willerton
DOI: https://doi.org/10.48550/arXiv.0807.0658
#diagram #formal_logic #hopf_algebra #hopf_monad #string_diagrams
#my_bibtex
A diagrammatic approach to Hopf monads

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.

arXiv.org