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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
On the equivalence of all models for (∞,2)-categories
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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