ω-weak equivalences between weak ω-categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144642" target="_blank" >RIV/00216224:14310/25:00144642 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0001870825003883" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0001870825003883</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2025.110490" target="_blank" >10.1016/j.aim.2025.110490</a>

Result language
angličtina
Original language name
ω-weak equivalences between weak ω-categories
Original language description
We study ω-weak equivalences between weak ω-categories in the sense of Batanin-Leinster. Our ω-weak equivalences are strict ω-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict ω-categories, they coincide with the weak equivalences in the model category of strict ω-categories defined by Lafont, Métayer, and Worytkiewicz. We show that the class of ω-weak equivalences has the 2-out-of-3 property. We also consider a generalisation of ω-weak equivalences, defined as weak ω-functors (in the sense of Garner) satisfying essential surjectivity, and show that this class also has the 2-out-of-3 property.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA22-02964S" target="_blank" >GA22-02964S: Enriched categories and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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