∞ -operads as symmetric monoidal ∞ -categories

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...

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Detalhes bibliográficos
Autores: Haugseng, Rune|||0000-0001-6468-362X, Kock, Joachim|||0000-0003-3358-2812
Tipo de documento: artigo
Data de publicação:2024
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:286798
Acesso em linha:https://ddd.uab.cat/record/286798
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6812406
Access Level:Acceso aberto
Palavra-chave:∞-operads
Symmetric monoidal ∞-categories
Descrição
Resumo: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.