On the equivalence of all models for (∞,2)-categories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00562929" target="_blank" >RIV/67985840:_____/22:00562929 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1112/jlms.12614" target="_blank" >https://doi.org/10.1112/jlms.12614</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/jlms.12614" target="_blank" >10.1112/jlms.12614</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the equivalence of all models for (∞,2)-categories

Popis výsledku v původním jazyce

The goal of this paper is to provide the last equivalence needed in order to identify all known models for (Formula presented.) -categories. We do this by showing that Verity's model of saturated 2-trivial complicial sets is equivalent to Lurie's model of (Formula presented.) -bicategories, which, in turn, has been shown to be equivalent to all other known models for (Formula presented.) -categories. A key technical input is given by identifying the notion of (Formula presented.) -bicategories with that of weak (Formula presented.) -bicategories, a step which allows us to understand Lurie's model structure in terms of Cisinski–Olschok's theory. Several of our arguments use tools coming from a new theory of outer (co)-Cartesian fibrations, further developed in a companion paper. In the last part of the paper, we construct a homotopically fully faithful scaled simplicial nerve functor for 2-categories, give two equivalent descriptions of it, and show that the homotopy 2-category of an (Formula presented.) -bicategory retains enough information to detect thin 2-simplices.

Název v anglickém jazyce

On the equivalence of all models for (∞,2)-categories

Popis výsledku anglicky

The goal of this paper is to provide the last equivalence needed in order to identify all known models for (Formula presented.) -categories. We do this by showing that Verity's model of saturated 2-trivial complicial sets is equivalent to Lurie's model of (Formula presented.) -bicategories, which, in turn, has been shown to be equivalent to all other known models for (Formula presented.) -categories. A key technical input is given by identifying the notion of (Formula presented.) -bicategories with that of weak (Formula presented.) -bicategories, a step which allows us to understand Lurie's model structure in terms of Cisinski–Olschok's theory. Several of our arguments use tools coming from a new theory of outer (co)-Cartesian fibrations, further developed in a companion paper. In the last part of the paper, we construct a homotopically fully faithful scaled simplicial nerve functor for 2-categories, give two equivalent descriptions of it, and show that the homotopy 2-category of an (Formula presented.) -bicategory retains enough information to detect thin 2-simplices.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of the London Mathematical Society

ISSN

0024-6107

e-ISSN

1469-7750

Svazek periodika

106

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

63

Strana od-do

1920-1982

Kód UT WoS článku

000792051000001

EID výsledku v databázi Scopus

2-s2.0-85129742099