Mathematische Zeitschrift

, Volume 281, Issue 3–4, pp 807–848 | Cite as

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

  • Dimitri AraEmail author
  • Moritz Groth
  • Javier J. Gutiérrez


We study the \((\infty , 1)\)-category of autoequivalences of \(\infty \)-operads. Using techniques introduced by Toën, 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 \(\mathbf {Z}/2\mathbf {Z}\). 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Dimitri Ara
    • 1
    Email author
  • Moritz Groth
    • 1
  • Javier J. Gutiérrez
    • 1
  1. 1.Institute for Mathematics, Astrophysics and Particle PhysicsRadboud Universiteit NijmegenNijmegenThe Netherlands

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