On notions of compactness, object classifiers, and weak Tarski universes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134290" target="_blank" >RIV/00216224:14310/23:00134290 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/S0960129523000051" target="_blank" >https://doi.org/10.1017/S0960129523000051</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129523000051" target="_blank" >10.1017/S0960129523000051</a>

Result language
angličtina
Original language name
On notions of compactness, object classifiers, and weak Tarski universes
Original language description
We prove a correspondence between kappa-small fibrations in simplicial presheaf categories equipped with the injective or projective model structure (and left Bousfield localizations thereof) and relatively kappa-compact maps in their underlying quasi-categories for suitably large regular cardinals kappa. We thus obtain a transition result between weakly universal small fibrations in the (type-theoretic) injective Dugger-Rezk-style standard presentations of model toposes and object classifiers in Grothendieck infinity-toposes in the sense of Lurie.
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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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