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math.CT2026
The points of canonical extensions of doctrines
Sam van Gool, Joshua L. Wrigley
We analyse the space of points of the canonical extension of a coherent doctrine. We first give a full characterisation of doctrine morphisms that are extensible, and relate it to…
math.CT2026
Locales in presheaf toposes vs. presheaves of locales
Vasileios Aravantinos-Sotiropoulos, Panagis Karazeris, Joshua Wrigley
By a well-known characterisation, in a presheaf topos every internal suplattice is a presheaf of suplattices, but not every presheaf of suplattices is an internal suplattice (and s…
math.CT2026
Generic bundles over a localic category
Graham Manuell, Joshua L. Wrigley
In this paper we construct classifying localic categories and groupoids for various bundles equipped with logical structure. When these bundles are local homeomorphisms, we recover…