Jérémie Marquès

works on

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

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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…