Jérémie Marquès

activity

20242026

collaborators

7 papers

math.LO2026

Compact-Open Dualities for Stably Continuous Posets

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

Jérémie Marquès

Constant domain intuitionistic logic admits a complete semantics in presheaf toposes, by interpreting sorts as constant presheaves and predicates as arbitrary sub-presheaves. The g…

math.CT2025

Poset-enriched pretoposes and compact ordered spaces

Jérémie Marquès, 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

Silvio Ghilardi, Jérémie Marquès

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…

cs.LO2025

First-Order Modal Logic via Logical Categories

Silvio Ghilardi, Jérémie Marquès

We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background…

math.CT2024

A Criterion for Categories on which every Grothendieck Topology is Rigid

Jérémie Marquès

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

math.CT2024

Atomic Toposes with Co-Well-Founded Categories of Atoms

Jérémie Marquès

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…