From Operads to Dendroidal Sets

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.

Written for an AMS volume on Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

References in corpus (6)

• Higher Topos Theory
• Dendroidal Sets
• Dendroidal sets and simplicial operads
• Dendroidal sets as models for homotopy operads
• Derived Algebraic Geometry III: Commutative Algebra
• Dold-Kan correspondence for dendroidal abelian groups

Cited by in corpus (1)

• Infinity Properads and Infinity Wheeled Properads