∞ -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...
| Autores: | , |
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| 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 |
| 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. |
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