Rectification of dendroidal left fibrations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917956532830208 |
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| author | Pratali, Francesca |
| author_facet | Pratali, Francesca |
| contents | For a discrete colored operad $P$, we construct an adjunction between the category of dendroidal sets over the nerve of $P$ and the category of simplicial $P$-algebras, and prove that when $P$ is $Σ$-free it establishes a Quillen equivalence with respect to the covariant model structure on the former category and the projective model structure on the latter. When $P=A$ is a discrete category, this recovers a Quillen equivalence previously established by Heuts-Moerdijk, of which we provide an independent proof.
To prove the constructed adjunction is a Quillen equivalence, we show that the left adjoint presents a previously established operadic straightening equivalence between $\infty$-categories. This involves proving that, for a discrete symmetric monoidal category $A$, the Heuts-Moerdijk equivalence is a monoidal equivalence of monoidal Quillen model categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rectification of dendroidal left fibrations Pratali, Francesca Algebraic Topology 18N45, 55P48, 18N40, 05C05, 18N70 For a discrete colored operad $P$, we construct an adjunction between the category of dendroidal sets over the nerve of $P$ and the category of simplicial $P$-algebras, and prove that when $P$ is $Σ$-free it establishes a Quillen equivalence with respect to the covariant model structure on the former category and the projective model structure on the latter. When $P=A$ is a discrete category, this recovers a Quillen equivalence previously established by Heuts-Moerdijk, of which we provide an independent proof. To prove the constructed adjunction is a Quillen equivalence, we show that the left adjoint presents a previously established operadic straightening equivalence between $\infty$-categories. This involves proving that, for a discrete symmetric monoidal category $A$, the Heuts-Moerdijk equivalence is a monoidal equivalence of monoidal Quillen model categories. |
| title | Rectification of dendroidal left fibrations |
| topic | Algebraic Topology 18N45, 55P48, 18N40, 05C05, 18N70 |
| url | https://arxiv.org/abs/2502.17415 |