Jérémie Marquès

works on

boolean pretopos 1 constant domain logic 1 discrete locales 1 intuitionistic logic 1 presheaf toposes 1 topos theory 1

From the 1 of 7 linked papers with an AI index.

collaborators

7 papers

math.LO2026

Compact-Open Dualities for Stably Continuous Posets

JÃ©rÃ©mie MarquÃ¨s, Jérémie Marquès

We organize and generalize several dualities involving continuous posets. The main theorem reads $\mathbf{St}_α\mathbf{Inf}_{α'}\mathbf{Cont}_{β'}\mathbf{Sup}_β\simeq (\mathbf{St}_…

math.LO2026

The Constant Domain Axiom in Toposes

JÃ©rÃ©mie MarquÃ¨s

The paper shows that the constant domain axiom for intuitionistic logic can be modeled in any topos using objects that are covert and Hausdorff as discrete locales, and proves that…

math.CT2025

A Criterion for Categories on which every Grothendieck Topology is Rigid

JÃ©rÃ©mie MarquÃ¨s

Let $C$ be a Cauchy-complete category. The subtoposes of $[C^{op}, Set]$ are sometimes all of the form $[D^{op}, Set]$ …

math.CT2025

Poset-enriched pretoposes and compact ordered spaces

JÃ©rÃ©mie MarquÃ¨s, Luca Reggio

We provide a characterisation of the category $KOrd$ of Nachbin's compact ordered spaces as a poset-enriched category. Up to equivalence, $KOrd$ is the only non-d…

math.CT2025

A Completeness Theorem for Topological Doctrines

We extend logical categories with fiberwise interior and closure operators so as to obtain an embedding theorem into powers of the category of topological spaces. The required axio…

math.CT2025

Atomic Toposes with Co-Well-Founded Categories of Atoms

The atoms of the Schanuel topos can be described as the pairs $(n, G)$ where $n$ is a finite set and $G$ is a subgroup of $Aut (n)$ . We give a general criterion on an…