∞-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...
| Autores: | , |
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| 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 |
| 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. |
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