  Functors from (co)operads to bialgebras relate Hopf algebras that occur in renormalisation to operads, which simplifies the proof of the Hopf algebra axioms, and induces a characterisation of the corresponding group of characters and Lie algebra of primitives of the dual in terms of the operad. In addition, it is shown that the Wick rotation formula leads to canonical algebras for one of these operads. 
Operads and the Hopf algebras of renormalisation