On autoequivalences of the (∞, 1)-category of ∞-operads

Abstract

We study the (∞, 1)-category of autoequivalences of ∞-operads. Using techniques introduced by Toën, Lurie, and Barwick and Schommer-Pries, we prove that this (∞, 1)-category is a contractible ∞-groupoid. Our calculation is based on the model of complete dendroidal Segal spaces introduced by Cisinski and Moerdijk. Similarly, we prove that the (∞, 1)-category of autoequivalences of non-symmetric ∞-operads is the discrete monoidal category associated to Z/2Z. We also include a computation of the (∞, 1)-category of autoequivalences of (∞, n)-categories based on Rezk’s Θn-spaces.