Generalised mixed distributive laws and Hopf-Borel type theorem for operads (original) (raw)

arXiv: Combinatorics, 2017

Abstract

In 2008, Loday generalises Hopf-Borel theorem to operads. We extend here his result by loosening and reducing hypotheses of this theorem to a class of rewriting rules generalising the classical notion of mixed distributive laws, that we call generalised mixed distributive laws. This enables us to show that for any operads P and Q having the same underlying S-module, there exists a generalised mixed distributive law lambda\lambdalambda such that any connected P coQ-bialgebra satisfying lambda\lambdalambda is free and cofree over its primitive elements. Our reasoning permits us to generate many new examples, while recovering the known ones by considering dual relations.

Bérénice Oger hasn't uploaded this paper.

Let Bérénice know you want this paper to be uploaded.

Ask for this paper to be uploaded.