Dold-Kan correspondence for dendroidal abelian groups

TL;DR

This paper extends the classical Dold-Kan correspondence to dendroidal abelian groups, establishing an equivalence with a category of dendroidal complexes, thus broadening the algebraic tools available for operadic structures.

Contribution

It introduces a Dold-Kan type correspondence for dendroidal abelian groups, expanding the classical theory to a new categorical context.

Findings

Established an equivalence between dendroidal abelian groups and dendroidal complexes

Extended classical Dold-Kan correspondence to operadic structures

Provides a new framework for algebraic analysis of dendroidal objects

Abstract

We prove a Dold-Kan type correspondence between the category of dendroidal abelian groups and a suitably constructed category of dendroidal complexes. Our result naturally extends the classical Dold-Kan correspondence between the category of simplicial abelian groups and the category of non-negatively graded chain complexes.