Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees - Gálvez-Carrillo, Imma; Kock, Joachim; Tonks, Andrew (Advances in mathematics (New York. 1965), 2014)
We prove a Faà di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids.