## 7 Citations

### Monoidal Grothendieck Construction

- Mathematics
- 2018

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.

- Mathematics
- 2018

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

- Mathematics
- 2019

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

- Mathematics
- 2021

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

- MathematicsACT
- 2019

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

- Mathematics
- 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…

### Topology from enrichment: the curious case of partial metrics

- Mathematics
- 2016

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…

## References

SHOWING 1-10 OF 27 REFERENCES

### The Grothendieck Construction and Gradings for Enriched Categories

- Mathematics
- 2009

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…

### TWO-SIDED DISCRETE FIBRATIONS IN 2-CATEGORIES AND BICATEGORIES

- Mathematics
- 2010

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…

### The comprehension construction

- Mathematics
- 2017

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

- MathematicsAppl. 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

- Mathematics
- 2008

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

- Mathematics
- 2010

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…