From Operads to Dendroidal Sets

Details From Operads to Dendroidal Sets From Operads to Dendroidal Sets

2010-12-20

arxiv.org/abs/1012.4315v3

Mathematical foundations of quantum field theory and perturbative string theory, 31-70, Proc. Sympos. Pure Math., 83, Amer. Ma

Mathematics

Algebraic Topology

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

Scientific paper

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.

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