Graphical calculus of Hopf crossed modules

Abstract

We give the graphical notion of crossed modules of Hopf algebras-will be called Hopf crossed modules for short-in a symmetric monoidal category. We use the web proof assistant Globular to visualize our (colored) string diagrams. As an application, we introduce the homotopy of Hopf crossed module maps via Globular, and give some of its functorial relations.

On the mod p Steenrod algebra and the Leibniz-Hopf algebra

“…There are also a wide variety of Hopf algebras with different rich algebraic structures. For some of these algebras we refer to [4,7,14,17,26].…”