Monoidal Envelopes of Families of $\infty$-Operads and $\infty$-Operadic Kan Extensions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912490947870720 |
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| author | Arakawa, Kensuke |
| author_facet | Arakawa, Kensuke |
| contents | We provide details of the proof of Lurie's theorem on operadic Kan extensions. Along the way, we generalize the construction of monoidal envelopes of $\infty$-operads to families of $\infty$-operads and use it to construct the fiberwise direct sum functor, both of which we characterize by certain universal properties. Aside from their uses in the proof of Lurie's theorem, these results and constructions have their independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10813 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Monoidal Envelopes of Families of $\infty$-Operads and $\infty$-Operadic Kan Extensions Arakawa, Kensuke Category Theory Algebraic Topology 18N70, 55P48 We provide details of the proof of Lurie's theorem on operadic Kan extensions. Along the way, we generalize the construction of monoidal envelopes of $\infty$-operads to families of $\infty$-operads and use it to construct the fiberwise direct sum functor, both of which we characterize by certain universal properties. Aside from their uses in the proof of Lurie's theorem, these results and constructions have their independent interest. |
| title | Monoidal Envelopes of Families of $\infty$-Operads and $\infty$-Operadic Kan Extensions |
| topic | Category Theory Algebraic Topology 18N70, 55P48 |
| url | https://arxiv.org/abs/2303.10813 |