Profinite ∞-operads

Thomas Blom, Ieke Moerdijk*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We show that a profinite completion functor for (simplicial or topological) operads with good homotopical properties can be constructed as a left Quillen functor from an appropriate model category of ∞-operads to a certain model category of profinite ∞-operads. The construction is based on a notion of lean ∞-operad, and we characterize those ∞-operads weakly equivalent to lean ones in terms of homotopical finiteness properties. Several variants of the construction are also discussed, such as the cases of unital (or closed) ∞-operads and of ∞-categories.

Original languageEnglish
Article number108601
Number of pages50
JournalAdvances in Mathematics
Publication statusPublished - 29 Oct 2022


  • Dendroidal sets
  • Infinity-operads
  • Lean infinity-operads
  • Profinite completion
  • Quillen model categories


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