On the equivalence of all models for (oo,2)-categories
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10454769" target="_blank" >RIV/00216208:11320/22:10454769 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=mRBFJrnFv_" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=mRBFJrnFv_</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.12614" target="_blank" >10.1112/jlms.12614</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On the equivalence of all models for (oo,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 (oo,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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
<a href="/cs/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
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