Relative operads model $\infty$-operads
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914207196250112 |
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| author | Arakawa, Kensuke Carmona, Victor Pratali, Francesca |
| author_facet | Arakawa, Kensuke Carmona, Victor Pratali, Francesca |
| contents | Given a (colored) operad and a set of unary operations, we can form an associated $\infty$-operad via localization. We show that localization determines an equivalence of homotopy theories of relative operads and $\infty$-operads. As an application, we give an affirmative answer to an open question by Harpaz, proving that Lurie's operadic nerve functor determines an equivalence of homotopy theories of simplicial operads and Lurie's $\infty$-operads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative operads model $\infty$-operads Arakawa, Kensuke Carmona, Victor Pratali, Francesca Algebraic Topology Category Theory 18Nxx, 18N55, 18N70, 18M60, 18M75, 55U35 Given a (colored) operad and a set of unary operations, we can form an associated $\infty$-operad via localization. We show that localization determines an equivalence of homotopy theories of relative operads and $\infty$-operads. As an application, we give an affirmative answer to an open question by Harpaz, proving that Lurie's operadic nerve functor determines an equivalence of homotopy theories of simplicial operads and Lurie's $\infty$-operads. |
| title | Relative operads model $\infty$-operads |
| topic | Algebraic Topology Category Theory 18Nxx, 18N55, 18N70, 18M60, 18M75, 55U35 |
| url | https://arxiv.org/abs/2512.16374 |