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Abstract |
We introduce Feynman categories and show that they naturally define bi-algebras.
In good circumstances these bi-algebras have Hopf quotients.
Corresponding to several levels of sophistication and decoration (both terms have technical definitions), we recover the Hopf algebras
of Goncharov and Brown from number theory, a Hopf algebra of Baues used in the analysis of double loop
spaces and the various Hopf algebras of Connes-Kreimer used in QFT as examples of the general theory.
Co-actions also appear naturally in this context as we will explain. |
