## 11 Citations

### Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories

- Mathematics
- 2022

A BSTRACT . We show that the free construction from multicategories to permuta- tive categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced…

### Multicategories Model All Connective Spectra

- Mathematics
- 2021

There is a free construction from multicategories to permutative categories, left adjoint to the endomorphism multicategory construction. The main result shows that these functors induce an…

### Extending homotopy theories across adjunctions

- Mathematics
- 2015

Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We…

### Multifunctorial inverse K-theory

- MathematicsAnnals of K-Theory
- 2022

A BSTRACT . We show that Mandell’s inverse K -theory functor is a categorically- enriched non-symmetric multifunctor. In particular, it preserves algebraic structures parametrized by non-symmetric…

### Coherence for braided and symmetric pseudomonoids

- MathematicsArXiv
- 2017

It is shown that these biequivalences categorify results in the theory of monoids and commutative monoids, and generalise standard coherence theorems for braided and symmetric monoidal categories.

### 2-categorical opfibrations, Quillen's Theorem B, and $S^{-1}S$

- Mathematics
- 2020

In this paper we show that the strict and lax pullbacks of a 2-categorical opfibration along an arbitrary 2-functor are homotopy equivalent. We give two applications. First, we show that the strict…

### A T ] 5 A pr 2 01 7 STABLE POSTNIKOV DATA OF PICARD 2-CATEGORIES

- Mathematics
- 2020

Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category D is an infinite loop space, the zeroth space of the K-theory…

### Stable Postnikov data of Picard 2-categories

- Mathematics
- 2016

Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category $\mathcal{D}$ is an infinite loop space, the zeroth space of…

### Supergeometry in Mathematics and Physics

- Physics, MathematicsNew Spaces in Physics
- 2015

This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it…

## References

SHOWING 1-10 OF 51 REFERENCES

### SYMMETRIC MONOIDAL CATEGORIES MODEL ALL CONNECTIVE SPECTRA

- Mathematics
- 1995

The classical innite loopspace machines in fact induce an equivalence of categories between a localization of the category of symmetric monoidal categories and the stable homotopy category of…

### Formal category theory: adjointness for 2-categories

- Mathematics, Philosophy
- 1974

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### An inverse $K$-theory functor

- MathematicsDocumenta Mathematica
- 2010

Thomason showed that the K-theory of symmetric monoidal categories models all connective spectra. This paper describes a new construction of a permutative category from a Gamma-space, which is then…

### Spectra associated to symmetric monoidal bicategories

- Mathematics
- 2012

We show how to construct a Gamma-bicategory from a symmetric monoidal bicategory, and use that to show that the classifying space is an infinite loop space upon group completion. We also show a way…

### Quasistrict symmetric monoidal 2-categories via wire diagrams

- Mathematics
- 2014

In this paper we give an expository account of quasistrict symmetric monoidal 2-categories, as introduced by Schommer-Pries. We reformulate the definition using a graphical calculus called wire…

### A model for the homotopy theory of homotopy theory

- Mathematics
- 1998

We describe a category, the objects of which may be viewed as models for homotopy theories. We show that for such models, “functors between two homotopy theories form a homotopy theory”, or more…

### Extending homotopy theories across adjunctions

- Mathematics
- 2015

Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We…

### Homotopy theory of higher categories

- Mathematics
- 2011

This is the first draft of a book about higher categories approached by iterating Segal's method, as in Tamsamani's definition of $n$-nerve and Pelissier's thesis. If $M$ is a tractable left proper…

### MODELING STABLE ONE-TYPES

- Mathematics
- 2012

Classication of homotopy n-types has focused on developing algebraic categories which are equivalent to categories of n-types. We expand this theory by providing algebraic models of…

### Bicategorical homotopy pullbacks

- Mathematics
- 2014

The homotopy theory of higher categorical structures has become a relevant part of the machinery of algebraic topology and algebraic K-theory, and this paper contains contributions to the study of…