The enriched Grothendieck construction

  title={The enriched Grothendieck construction},
  author={Jonathan Beardsley and Liang Ze Wong},
  journal={Advances in Mathematics},

Monoidal Grothendieck Construction

We lift the standard equivalence between fibrations and indexed categories to an equivalence between monoidal fibrations and monoidal indexed categories, namely weak monoidal pseudofunctors to the

On Enriched Fibrations.

We introduce the notion of an enriched fibration, i.e. a fibration whose total category and base category are enriched in those of a monoidal fibration in an appropriate way. Furthermore, we provide

The genuine operadic nerve

We construct a generalization of the operadic nerve, providing a translation between the equivariant simplicially enriched operadic world to the parametrized $\infty$-categorical perspective. This

2-Dimensional Categories

2-Dimensional Categories provides an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a

Enriched Lawvere Theories for Operational Semantics

This work illustrates the ideas of enriched theories with the SKI-combinator calculus, a variable-free version of the lambda calculus that lets us study all models of all enriched theories in all contexts in a single category.

The Operadic Nerve, Relative Nerve, and the Grothendieck Construction

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

Topology from enrichment: the curious case of partial metrics

For any small quantaloid $\Q$, there is a new quantaloid $\D(\Q)$ of diagonals in $\Q$. If $\Q$ is divisible then so is $\D(\Q)$ (and vice versa), and then it is particularly interesting to compare



The Grothendieck Construction and Gradings for Enriched Categories

The Grothendieck construction is a process to form a single category from a diagram of small categories. In this paper, we extend the definition of the Grothendieck construction to diagrams of small

The Grothendieck construction for model categories


Fibrations over a category B, introduced to category theory by Grothendieck, determine pseudo-functors B op ! Cat. A two-sided discrete variation models functors B op A! Set. By work of Street, both

Fibred 2-categories and bicategories

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

Yoneda Structures from 2-toposes

  • Mark Weber
  • Mathematics
    Appl. Categorical Struct.
  • 2007
A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the Yoneda structure it generates are explored and results enabling one to exhibit objects as cocomplete in the sense definable within a YonedA structure are presented.

Hochschild Cohomology of Presheaves as Map-Graded Categories

Building on the work of Gerstenhaber and Schack, we define the Hochschild complex of a presheaf (or a pseudofunctor) on a category as the Hochschild complex of an associated “-graded” category,

A Survey of (∞, 1)-Categories

In this paper we give a summary of the comparisons between different definitions of so-called (∞, 1)-categories, which are considered to be models for ∞-categories whose n-morphisms are all