∞-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 sets...

ver descrição completa

Detalhes bibliográficos
Autores: Haugseng, R., Kock, J.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/537582
Acesso em linha:http://hdl.handle.net/2072/537582
Access Level:acceso abierto
Palavra-chave:Symmetric monoidal ∞-categories
∞-operads
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. © 2024 Universitat Autonoma de Barcelona. All rights reserved.