Joshua L. Wrigley

I am a logician and category theorist, specialising in topos theory. I am currently a Marie Skłodowska-Curie postdoctoral fellow at Masarykova Univerzita, working with John Bourke on my project HiDimAFOL (Higher Dimensional Aspects of First Order Logic).

Previously, I was a post-doc at Université Paris Cité, working with Sam van Gool, and at Queen Mary University of London, working with Ivan Tomašić. Before that, I completed my PhD under the supervision of Olivia Caramello at the University of Insubria.

My research involves the interaction between mathematical logic, topology, and category theory. I am especially interested in topos-theoretic approaches to model theory.

E-mail: wrigley@math.muni.cz.

Generic bundles over a localic category, with Graham Manuell, Preprint (2025).

Existential completions and Herbrand's theorem, Theory and Applications of Categories, Vol. 45, No. 23, pp. 924-950 (2026).

Day algebras, with Edmund Robinson, Mathematical Structures in Computer Science, Vol. 36(6) (2026).

On topological groupoids that represent theories, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik: to appear (2026).

Topoi with enough points and topological groupoids, Journal of Pure and Applied Algbera, Vol. 229(10), 108073 (2025).

Ultracategories via Kan extensions of relative monads, with Umberto Tarantino, Preprint (2025).

Some properties of internal locale morphisms externalised, Theory and Applications of Categories, Vol. 41, No. 35, pp. 1160-1202 (2024).

The representing localic groupoid for a geometric theory, with Graham Manuell, Expositions in Theory and Applications of Categories No. 2 (2024).