Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees

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.

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Bibliographic Details
Published in:	Advances in mathematics (New York. 1965) Vol. 254; pp. 79 - 117
Main Authors:	Gálvez-Carrillo, Imma, Kock, Joachim, Tonks, Andrew
Format:	Journal Article Publication
Language:	English
Published:	Elsevier Inc 20.03.2014
Subjects:	05 Combinatorics 05C Graph theory 20 Group theory and generalizations 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) 81 Quantum theory 81T Quantum field theory; related classical field theories Bialgebras Classificació AMS Física matemàtica Grafs, Teoria de Graph theory Group theory Groupoids Grupoides Grups, Teoria de Homotopy cardinality Matemàtiques i estadística Mathematical physics Perturbative methods of renormalisation Polynomial functors Teoria de categories; àlgebra homològica Teoria de grups Trees Àlgebra Àrees temàtiques de la UPC Trees Polynomial functors Groupoids Homotopy cardinality Bialgebras Perturbative methods of renormalisation
ISSN:	0001-8708, 1090-2082
Online Access:	Get full text
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