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.

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On the theories classified by an étendue, Bulletin of the London Mathematical Society, Vol. 58, Issue 7, e70430 (2026).

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The points of canonical extensions of doctrines, with Sam van Gool, Preprint (2026).

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Locales in presheaf toposes vs. presheaves of locales, with Vasileios Aravantinos-Sotiropoulos and Panagis Karazeris, Preprint (2026).

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Generic bundles over a localic category, with Graham Manuell, Preprint (2026).

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

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

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On topological groupoids that represent theories, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, Vol. 72, pp. 1-44 (2026).

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

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

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

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