"When you gaze long enough into the abyss, you start noticing that the abyss has the structure of a Hopf algebra."
-- Udi Meir, at the start of his colloquium talk.
He followed it up with "Nietzsche phrased it a bit differently, but I am sure this is what he meant." What a fantastic start!
He talked about Zelevinsky's construction of a Hopf algebra out of the representations of the symmetric groups, and its generalisations.
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.
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.
Locally Trivial
nope