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arXiv · 1312.4994

On autoequivalences of the (\infty, 1)-category of \infty-operads

Dimitri Ara·Moritz Groth·Javier J. Gutiérrez
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Abstract

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

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Dimitri Ara, Moritz Groth, Javier J. Gutiérrez. 2013-12-17. On autoequivalences of the (\infty, 1)-category of \infty-operads. https://doi.org/10.1007/s00209-015-1509-5

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