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

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On the equivalence of all models for (oo,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&apos;s model of saturated 2-trivial complicial sets is equivalent to Lurie&apos;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&apos;s model structure in terms of Cisinski-Olschok&apos;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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    <a href="/en/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopy and Homology Methods and Tools Related to Mathematical Physics</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2022

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Journal of the London Mathematical Society

  • ISSN

    0024-6107

  • e-ISSN

    1469-7750

  • Volume of the periodical

    106

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    63

  • Pages from-to

    1920-1982

  • UT code for WoS article

    000792051000001

  • EID of the result in the Scopus database

    2-s2.0-85129742099