• Corpus ID: 118677251

The Operadic Nerve, Relative Nerve, and the Grothendieck Construction

  title={The Operadic Nerve, Relative Nerve, and the Grothendieck Construction},
  author={Jonathan Beardsley and Liang Ze Wong},
  journal={arXiv: Category Theory},
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… 

Thom Objects Are Cotorsors.

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

The enriched Grothendieck construction



On the Unicity of the Homotopy Theory of Higher Categories

We axiomatise the theory of $(\infty,n)$-categories. We prove that the space of theories of $(\infty,n)$-categories is a $B(\mathbb{Z}/2)^n$. We prove that Rezk's complete Segal $\Theta_n$-spaces,

The comprehension construction

In this paper we construct an analogue of Lurie's "unstraightening" construction that we refer to as the "comprehension construction". Its input is a cocartesian fibration $p \colon E \to B$ between

The enriched Grothendieck construction


  • G. M. Kelly
  • Mathematics
    Elements of ∞-Category Theory
  • 2005
Although numerous contributions from divers authors, over the past fifteen years or so, have brought enriched category theory to a developed state, there is still no connected account of the theory,

Derived Algebraic Geometry II: Noncommutative Algebra

1 Monoidal ∞-Categories 4 1.1 Monoidal Structures and Algebra Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Cartesian Monoidal Structures . . . . . . . . . . . . . . . . . .

Dwyer-Kan localization revisited

A version of Dwyer-Kan localization in the context of infinity-categories and simplicial categories is presented. Some results of the classical papers by Dwyer and Kan on simplicial localization are