From Operads to Dendroidal Sets

TL;DR

This paper reviews the development of dendroidal sets as a framework for studying $$-operads, highlighting their advantages over strict operads in modeling complex algebraic structures.

Contribution

It provides an overview of the current theory of dendroidal sets and demonstrates their application to $$-spaces and weak $n$-categories.

Findings

Dendroidal sets generalize simplicial sets for $$-operads.

They offer greater flexibility for modeling homotopy-coherent structures.

The framework facilitates the study of $A_{}$-spaces and weak $n$-categories.

Abstract

Dendroidal sets offer a formalism for the study of $\infty$-operads akin to the formalism of $\infty$-categories by means of simplicial sets. We present here an account of the current state of the theory while placing it in the context of the ideas that lead to the conception of dendroidal sets. We briefly illustrate how the added flexibility embodied in $\infty$-operads can be used in the study of $A_{\infty}$-spaces and weak $n$-categories in a way that cannot be realized using strict operads.