• Corpus ID: 118677251

The Operadic Nerve, Relative Nerve, and the Grothendieck Construction

@article{Beardsley2018TheON,
  title={The Operadic Nerve, Relative Nerve, and the Grothendieck Construction},
  author={Jonathan Beardsley and Liang Ze Wong},
  journal={arXiv: Category Theory},
  year={2018}
}
We relate the relative nerve $\mathrm{N}_f(\mathcal{D})$ of a diagram of simplicial sets $f \colon \mathcal{D} \to \mathsf{sSet}$ with the Grothendieck construction $\mathsf{Gr} F$ of a simplicial functor $F \colon \mathcal{D} \to \mathsf{sCat}$ in the case where $f = \mathrm{N} F$. We further show that any strict monoidal simplicial category $\mathcal{C}$ gives rise to a functor $\mathcal{C}^\bullet \colon \Delta^\mathrm{op} \to \mathsf{sCat}$, and that the relative nerve of $\mathrm{N… 

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Let $C$ be a symmetric monoidal quasicategory, and $R$ an $E_n$-algebra of $C$ equipped with an action of an $n$-fold loop space $G$. We prove that the derived quotient of $R$ with respect to this

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