∞ -operads as symmetric monoidal ∞ -categories

• Autores: Rune Haugseng, Joachim Kock
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 1, 2024, págs. 111-137
• Idioma: inglés
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• Resumen

  • We use Lurie’s symmetric monoidal envelope functor to give two new descriptions of ∞-operads: as certain symmetric monoidal ∞-categories whose underlying symmetric monoidal ∞-groupoids are free, and as certain symmetric monoidal ∞-categories equipped with a symmetric monoidal functor to finite sets (with disjoint union as tensor product). The latter leads to a third description of ∞-operads, as a localization of a presheaf ∞-category, and we use this to give a simple proof of the equivalence between Lurie’s and Barwick’s models for ∞-operads.