A categorical formulation of the Deligne-Terasoma approach to double shuffle theory

TL;DR

This paper introduces a bimodule with a factorization structure that provides a new algebraic interpretation of the geometric constructions in double shuffle theory, connecting Betti and de Rham coproducts.

Contribution

It presents a novel categorical framework (BFS) that unifies and interprets key geometric structures in double shuffle theory.

Findings

BFS induces an algebra morphism.

Provides an interpretation of Betti and de Rham coproducts.

Connects geometric and algebraic aspects of double shuffle theory.

Abstract

In this paper, we introduce the notion of a bimodule with a factorization structure (BFS) and show that such a structure gives rise to an algebra morphism. We then prove that this framework offers an interpretation of the geometric construction underlying both the Betti and de Rham harmonic coproducts of the double shuffle theory developed Enriquez-Furusho inspired by an unpublished preprint of Deligne-Terasoma.