On notions of compactness, object classifiers, and weak Tarski universes
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Mathematical Structures in Computer Science |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1017/S0960129523000051 |
| Doi | http://dx.doi.org/10.1017/S0960129523000051 |
| Keywords | relative compactness; object classifiers; Tarski universes; presentable 8-categories; combinatorial model categories |
| 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. |
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